Recent zbMATH articles in MSC 92D https://zbmath.org/atom/cc/92D 2022-06-24T15:10:38.853281Z Werkzeug Corrigendum to: The edge-product space of phylogenetic trees is not shellable'' https://zbmath.org/1485.05027 2022-06-24T15:10:38.853281Z "Stadnyk, Grace" https://zbmath.org/authors/?q=ai:stadnyk.grace From the text: The authors regret two pairs of elements in Fig. 1 in their paper [ibid. 135, Article ID 102311, 17 p. (2022; Zbl 1483.05024)] were inadvertently and incorrectly swapped. Tree topologies along a tropical line segment https://zbmath.org/1485.14118 2022-06-24T15:10:38.853281Z "Yoshida, Ruriko" https://zbmath.org/authors/?q=ai:yoshida.ruriko "Cox, Shelby" https://zbmath.org/authors/?q=ai:cox.shelby Summary: Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical metric. One of the challenges in applications of tropical geometry to tree spaces is the difficulty interpreting outcomes of statistical models with the tropical metric. This paper focuses on combinatorics of tree topologies along a tropical line segment, an intrinsic geodesic with the tropical metric, between two phylogenetic trees over the tree space and we show some properties of a tropical line segment between two trees. Specifically we show that a probability of a tropical line segment of two randomly chosen trees going through the origin (the star tree) is zero if the number of leave is greater than four, and we also show that if two given trees differ only one nearest neighbor interchange (NNI) move, then the tree topology of a tree in the tropical line segment between them is the same tree topology of one of these given two trees with possible zero branch lengths. Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment https://zbmath.org/1485.34041 2022-06-24T15:10:38.853281Z "Khan, Najeeb Alam" https://zbmath.org/authors/?q=ai:alam-khan.najeeb "Razzaq, Oyoon Abdul" https://zbmath.org/authors/?q=ai:razzaq.oyoon-abdul "Mondal, Sankar Parsad" https://zbmath.org/authors/?q=ai:mondal.sankar-parsad "Rubbab, Qammar" https://zbmath.org/authors/?q=ai:rubbab.qammar Summary: The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey-predator model with imprecise biological parameters and fractional order generalized Hukuhara (fgH) differentiability. In this vain, different possible systems of the model are constructed, according to the increasing and decreasing behavior of population growth. Feasibility and stability analyses of equilibrium points of the stated models are also discussed by means of variational matrix with Routh-Hurwitz conditions. In addition, the numerical elaborations are carried out by taking parametric expansion of fuzzy fractional Laplace transform (FFLT). This significantly helps the researchers in using a novel approach to analyze the constant solutions of the dynamical systems in the presence of fractional index. This would allow the avoidance of any intricacy that occurs while solving fractional order derivatives. Furthermore, this attempt also provides numerical and pictorial results, obtained through some well-known methods, namely fifth-forth Runge-Kutta method (FFRK), Grunwald-Letnikov's definition (GL) and Adams-Bashforth method (ABM) that are deemed appropriate to scrutinize the dynamics of the system of equations. Smoothing a piecewise-smooth: an example from plankton population dynamics https://zbmath.org/1485.34075 2022-06-24T15:10:38.853281Z "Piltz, Sofia H." https://zbmath.org/authors/?q=ai:piltz.sofia-h Summary: We discuss a piecewise-smooth dynamical system inspired by plankton observations and constructed for one predator switching its diet between two different types of prey. We then discuss two smooth formulations of the piecewise-smooth model obtained by using a hyperbolic tangent function and adding a dimension to the system. We compare model behaviour of the three systems and show an example case where the steepness of the switch is determined from a comparison with data on freshwater plankton. For the entire collection see [Zbl 1368.00047]. Existence theory and numerical simulation of HIV-I cure model with new fractional derivative possessing a non-singular kernel https://zbmath.org/1485.34130 2022-06-24T15:10:38.853281Z "Aliyu, Aliyu Isa" https://zbmath.org/authors/?q=ai:aliyu.aliyu-isa "Alshomrani, Ali Saleh" https://zbmath.org/authors/?q=ai:alshomrani.ali-saleh "Li, Yongjin" https://zbmath.org/authors/?q=ai:li.yongjin "Inc, Mustafa" https://zbmath.org/authors/?q=ai:inc.mustafa "Baleanu, Dumitru" https://zbmath.org/authors/?q=ai:baleanu.dumitru-i Summary: In this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana-Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard-Lindelöf has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane $$\mathbb{R}_+^3$$ is a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic. A predator-prey system with generalized Holling type IV functional response and Allee effects in prey https://zbmath.org/1485.34131 2022-06-24T15:10:38.853281Z "Arsie, Alessandro" https://zbmath.org/authors/?q=ai:arsie.alessandro "Kottegoda, Chanaka" https://zbmath.org/authors/?q=ai:kottegoda.chanaka "Shan, Chunhua" https://zbmath.org/authors/?q=ai:shan.chunhua Summary: The transition between strong and weak Allee effects in prey provides a simple regime shift in ecology. In this paper, we study the interplay between the functional response of Holling type IV and both strong and weak Allee effects. The model investigated here presents complex dynamics and high codimension bifurcations. In particular, nilpotent cusp singularity of order 3 and degenerate Hopf bifurcation of codimension 3 are completely analyzed. Remarkably it is the first time that three limit cycles are discovered in predator-prey models with multiplicative Allee effects. Moreover, a new unfolding of nilpotent saddle of codimension 3 with a fixed invariant line is discovered and fully developed, and the existence of codimension 2 heteroclinic bifurcation is proven. Our work extends the existing results of predator-prey systems with Allee effects. The bifurcation analysis and diagram allow us to give biological interpretations of predator-prey interactions. Global asymptotic stability of a general fractional-order single-species model https://zbmath.org/1485.34135 2022-06-24T15:10:38.853281Z "Hoang, Manh Tuan" https://zbmath.org/authors/?q=ai:hoang.manh-tuan Summary: In this work, we introduce a general fractional-order single-species model and study its dynamical qualitative properties. This model is derived from a well-known integer-order single-species model and the Caputo fractional derivative. We propose a new and simple approach to establish the global asymptotic stability (GAS) of the proposed model. This approach is not based on the Lyapunov stability theory but on nonstandard techniques of mathematical analysis for fractional dynamical systems. The main result is that the GAS and monotone convergence of the fractional-order model are determined fully. To show the advantage of the new approach, we consider a generalized version of the fractional-order single-species model and analyze its GAS by the new approach. As we expected, the GAS of the generalized version is also established. As an important consequence, the GAS of a well-known fractional-order logistic equation is obtained. This result provides an important improvement for the results constructed in a previous work [\textit{A. M. A. El-Sayed} et al., Appl. Math. Lett. 20, No. 7, 817--823 (2007; Zbl 1140.34302)]. It is worth noting that the new approach can be also applied to study the GAS of extended versions of the integer-order single-species model in the context of other fractional derivatives. Finally, some numerical examples are performed to illustrate and support the theoretical results. SIRS epidemiological model with ratio-dependent incidence: influence of preventive vaccination and treatment control strategies on disease dynamics https://zbmath.org/1485.34136 2022-06-24T15:10:38.853281Z "Kumar, Udai" https://zbmath.org/authors/?q=ai:kumar.udai "Mandal, Partha Sarathi" https://zbmath.org/authors/?q=ai:mandal.partha-sarathi "Tripathi, Jai Prakash" https://zbmath.org/authors/?q=ai:tripathi.jai-prakash "Bajiya, Vijay Pal" https://zbmath.org/authors/?q=ai:bajiya.vijay-pal "Bugalia, Sarita" https://zbmath.org/authors/?q=ai:bugalia.sarita Summary: In this paper, we study an SIRS epidemic model with ratio-dependent incidence rate function describing the mechanisms of infectious disease transmission. Impacts of vaccination and treatment on the transmission dynamics of the disease have been explored. The treatment rate is constant when the number of infected individuals is greater than the maximal capacity of treatment and proportional to the number of infected individuals when the number of infected individuals is less than the maximal capacity of treatment. Analysis shows that (1) the sufficiently large value of the preventive vaccination rate can control the spread of disease, and (2) a threshold level of the psychological (or inhibitory) effects in the incidence rate function is enough to decrease the infective population. It is also obtained that model undergoes transcritical and saddle-node bifurcations with respect to disease contact rate. Moreover, in the presence of treatment strategy, the model has multiple endemic equilibria and undergoes a backward bifurcation. The maximal capacity of treatment plays important roles on the disease dynamics of the model. The number of infected individuals decreases with respect to the maximal capacity of treatment, and the disease completely dies out from the system for the large capacity of the treatment when constant treatment strategy is applied. Further, it is also found that the spread of disease can be suppressed by increasing treatment rate. From sensitivity analysis, we have observed that the transmission and treatment rates are most sensitive parameters. The effects of different parameters on the disease dynamics have also been investigated via numerical simulation. Bounded global Hopf branches for stage-structured differential equations with unimodal feedback https://zbmath.org/1485.34175 2022-06-24T15:10:38.853281Z "Shu, Hongying" https://zbmath.org/authors/?q=ai:shu.hongying "Wang, Lin" https://zbmath.org/authors/?q=ai:wang.lin "Wu, Jianhong" https://zbmath.org/authors/?q=ai:wu.jianhong New findings on exponential convergence of a Nicholson's blowflies model with proportional delay https://zbmath.org/1485.34188 2022-06-24T15:10:38.853281Z "Xu, Changjin" https://zbmath.org/authors/?q=ai:xu.changjin "Li, Peiluan" https://zbmath.org/authors/?q=ai:li.peiluan "Yuan, Shuai" https://zbmath.org/authors/?q=ai:yuan.shuai Summary: We deal with Nicholson's blowflies model with proportional delays. Employing the differential inequality theory, we give a new sufficient condition that guarantees the exponential convergence of all solutions of Nicholson's blowflies model with proportional delays. Numerical simulations are put into effect to examine our theoretical findings. The derived results of this manuscript are innovative and complement some known investigations. Criteria of global attraction in systems of delay differential equations with mixed monotonicity https://zbmath.org/1485.34190 2022-06-24T15:10:38.853281Z "El-Morshedy, Hassan A." https://zbmath.org/authors/?q=ai:el-morshedy.hassan-a "Ruiz-Herrera, Alfonso" https://zbmath.org/authors/?q=ai:ruiz-herrera.alfonso Summary: In this paper we extend the classical decomposing+embedding'' method for systems of delay differential equations. Our extension has two advantages: (1) enhancing the range of applicability of the classical method and (2) providing delay dependent criteria of global attraction. The leading ideas are, on the one hand, the extension of the notion of dominance introduced first for difference equations and, on the other hand, the use of some monotone ideas developed by H. L. Smith and collaborators. We apply our results to some classical models of population dynamics, mainly models with patch structure. Stochastic delay differential neoclassical growth model https://zbmath.org/1485.34204 2022-06-24T15:10:38.853281Z "Wang, Wentao" https://zbmath.org/authors/?q=ai:wang.wentao "Chen, Wei" https://zbmath.org/authors/?q=ai:chen.wei|chen.wei.2|chen.wei.1|chen.wei.3|chen.wei.4 Summary: Focusing on delay differential neoclassical growth model in random environments, we introduce the stochastic model to describe the dynamics of the long-run behavior of the economy with a parameter perturbed by white noises. We prove that the global positive solution exists uniquely and estimate its ultimate boundedness in mean and sample Lyapunov exponent. Finally, some numerical tests are given to illustrate theoretical results. Correlated random walks in heterogeneous landscapes: derivation, homogenization, and invasion fronts https://zbmath.org/1485.35028 2022-06-24T15:10:38.853281Z "Lutscher, Frithjof" https://zbmath.org/authors/?q=ai:lutscher.frithjof "Hillen, Thomas" https://zbmath.org/authors/?q=ai:hillen.thomas Summary: Many models for the movement of particles and individuals are based on the diffusion equation, which, in turn, can be derived from an uncorrelated random walk or a position-jump process. In those models, individuals have a location but no well-defined velocity. An alternative, and sometimes more accurate, model is based on a correlated random walk or a velocity-jump process, where individuals have a well defined location and velocity. The latter approach leads to hyperbolic equations for the density of individuals, rather than parabolic equations that result from the diffusion process. Almost all previous work on correlated random walks considers a homogeneous landscape, whereas diffusion models for uncorrelated walks have been extended to spatially varying environments. In this work, we first derive the equations for a correlated random walk in a one-dimensional spatially varying environment with either smooth variation or piecewise constant variation. Then we show how to derive the so-called parabolic limit from the resulting hyperbolic equations. We develop homogenization theory for the hyperbolic equations, and show that taking the parabolic limit and homogenization are commuting actions. We illustrate our results with two examples from ecology: the persistence and spread of a population in a patchy heterogeneous landscape. Global solution and spatial patterns for a ratio-dependent predator-prey model with predator-taxis https://zbmath.org/1485.35044 2022-06-24T15:10:38.853281Z "Gao, Xiaoyan" https://zbmath.org/authors/?q=ai:gao.xiaoyan Summary: This paper analyzes the dynamic behavior of a ratio-dependent predator-prey model with predator-taxis, which the prey can move in the opposite direction of predator gradient. The first purpose is to prove rigorously the global existence and boundedness of the classical solution for the model based on the heat operator semigroup theory and some priori estimates. The another purpose is to analyze the stability of positive equilibrium, which the results will be extended to the case that the derivative of prey's functional response with prey is positive, and it will be found that large predator-taxis can stabilize equilibrium even diffusion-driven instability has occurred. Finally, the numerical simulations present that the pattern formation may arise and predator-taxis is the driving factor for the evolution of spatial inhomogeneity into homogeneity. On analytical solution of time-fractional biological population model by means of generalized integral transform with their uniqueness and convergence analysis https://zbmath.org/1485.35100 2022-06-24T15:10:38.853281Z "Rashid, Saima" https://zbmath.org/authors/?q=ai:rashid.saima "Ashraf, Rehana" https://zbmath.org/authors/?q=ai:ashraf.rehana "Bonyah, Ebenezer" https://zbmath.org/authors/?q=ai:bonyah.ebenezer Summary: This research utilizes the generalized integral transform and the Adomian decomposition method to derive a fascinating explicit pattern for outcomes of the biological population model (BPM). It assists us in comprehending the dynamical technique of demographic variations in BPMs and generates significant projections. Besides that, generalized integral transforms are the unification of other existing transforms. To investigate the closed form solutions, we employed a fractional complex transform to deal with a partial differential equation of fractional order and a generalized decomposition method was applied to analyze the nonlinear equation. Several aspects of the Caputo and Atangana-Baleanu fractional derivative operators are discussed with the aid of a generalized integral transform. In mathematical terms, the variety of equations and their solutions have been discovered and identified with various novel features of the projected model. To provide additional context for these ideas, numerous sorts of illustrations and tabulations are presented. The precision and efficacy of the proposed technique suggest that it can be used for a variety of nonlinear evolutionary problems. Propagation dynamics of a nonlocal periodic organism model with non-monotone birth rates https://zbmath.org/1485.35102 2022-06-24T15:10:38.853281Z "Bai, Zhenguo" https://zbmath.org/authors/?q=ai:bai.zhenguo "Zhang, Liang" https://zbmath.org/authors/?q=ai:zhang.liang|zhang.liang.3|zhang.liang.2|zhang.liang.1 Summary: This work is concerned with a nonlocal reaction-diffusion system modeling the propagation dynamics of organisms owning mobile and stationary states in periodic environments. We establish the existence of the asymptotic speed of spreading for the model system with monotone birth function via asymptotic propagation theory of monotone semiflow, and then discuss the case for non-monotone birth function by using the squeezing technique. In terms of the truncated problem on a finite interval, we apply the method of super- and sub-solutions and the fixed point theorem combined with regularity estimation and limit arguments to obtain the existence of time periodic traveling waves for the model system without quasi-monotonicity. The non-existence proof is to use the results of the spreading speed. Finally, as an application, we study the spatial dynamics of the model with the birth rate function of Ricker type and numerically demonstrate analytic results. Propagation phenomena for time-space periodic monotone semiflows and applications to cooperative systems in multi-dimensional media https://zbmath.org/1485.35106 2022-06-24T15:10:38.853281Z "Du, Li-Jun" https://zbmath.org/authors/?q=ai:du.lijun "Li, Wan-Tong" https://zbmath.org/authors/?q=ai:li.wan-tong "Shen, Wenxian" https://zbmath.org/authors/?q=ai:shen.wenxian Summary: The current paper is concerned with propagation phenomena for time-space periodic monotone semiflows and applications to time-space periodic cooperative systems in multi-dimensional media. We first establish some abstract theory on spreading speeds and traveling waves for time-space periodic monotone semiflows in the space of vector-valued functions on $$\mathbb{R}^N$$. Among others, we prove the equivalence of spreading speeds adopted by two different approaches, several spreading properties in terms of the spreading speeds, and the existence of periodic traveling waves which extends several known results in various special cases. By applying the abstract theory, we study the spreading speeds and traveling waves of time-space periodic cooperative systems in multi-dimensional media. It is proved that such a system admits a single spreading speed (resp. asymptotic spreading ray speed and asymptotic spreading set) under certain conditions. A set of sufficient conditions are also given for the single spreading speed to be linearly determinate. Furthermore, we show that the spreading speed can be characterized as the minimal wave speed of periodic traveling waves. The obtained results are then applied to the two-species periodic competition system in multi-dimensional media. Nonmonotonicity of traveling wave profiles for a unimodal recursive system https://zbmath.org/1485.35107 2022-06-24T15:10:38.853281Z "Fang, Jian" https://zbmath.org/authors/?q=ai:fang.jian "Pan, Yingli" https://zbmath.org/authors/?q=ai:pan.yingli Piecewise linear model of phytoplankton wave propagation in periodical vortex flow https://zbmath.org/1485.35108 2022-06-24T15:10:38.853281Z "Miroshnichenko, Taisia" https://zbmath.org/authors/?q=ai:miroshnichenko.taisia-p "Gubernov, Vladimir" https://zbmath.org/authors/?q=ai:gubernov.vladimir-vladimirovich "Minaev, Sergey" https://zbmath.org/authors/?q=ai:minaev.sergey-s "Mislavskii, Vladimir" https://zbmath.org/authors/?q=ai:mislavskii.vladimir "Okajima, Junnosuke" https://zbmath.org/authors/?q=ai:okajima.junnosuke Propagation dynamics for an age-structured population model in time-space periodic habitat https://zbmath.org/1485.35109 2022-06-24T15:10:38.853281Z "Pan, Yingli" https://zbmath.org/authors/?q=ai:pan.yingli Summary: How do environmental heterogeneity influence propagation dynamics of the age-structured invasive species? We investigate this problem by considering a yearly generation invasive species in time-space periodic habitat. Starting from an age-structured population growth law, we formulate a reaction-diffusion model with time-space periodic dispersal, mortality and recruitment. Thanks to the fundamental solution for linear part of the model, we reduce to study the dynamics of a time-space periodic semiflow which is defined by the solution map. By the recent developed dynamical theory in [\textit{J. Fang} et al., J. Funct. Anal. 272, No. 10, 4222--4262 (2017; Zbl 1398.35116)], we obtained the spreading speed and its coincidence with the minimal wave speed of time-space periodic traveling waves, as well as the variational characterization of spreading speed in terms of a principal eigenvalue problem. Such results are also proved back to the reaction-diffusion model. Spreading speeds and traveling waves for a time periodic DS-I-A epidemic model https://zbmath.org/1485.35110 2022-06-24T15:10:38.853281Z "Yang, Xiying" https://zbmath.org/authors/?q=ai:yang.xiying "Lin, Guo" https://zbmath.org/authors/?q=ai:lin.guo Summary: This paper is devoted to studying the speed of asymptotic spreading and minimal wave speed of traveling wave solutions for a time periodic and diffusive DS-I-A epidemic model, which describes the propagation threshold of disease spreading. The main feature of this model is the possible deficiency of the classical comparison principle such that many known results do not directly work. The speed of asymptotic spreading is estimated by constructing auxiliary equations and applying the classical theory of asymptotic spreading for Fisher type equation. The minimal wave speed is established by proving the existence and nonexistence of the nonconstant traveling wave solutions. Moreover, some numerical examples are presented to model the propagation dynamics of this system. On a predator-prey reaction-diffusion model with nonlocal effects https://zbmath.org/1485.35265 2022-06-24T15:10:38.853281Z "Han, Bang-Sheng" https://zbmath.org/authors/?q=ai:han.bang-sheng "Yang, Ying-Hui" https://zbmath.org/authors/?q=ai:yang.yinghui Summary: In this paper, we consider an initial value problem of a predator-prey system with integral term. By establishing comparison principle and constructing monotone sequences, the existence and uniqueness for the solution of that problem is proved. Then we further show the uniform boundedness. Finally, some conditions of Turing bifurcation occurring are given and illustrated by numerical simulations. Approximate solutions of the one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation with quasilocal competitive losses https://zbmath.org/1485.35360 2022-06-24T15:10:38.853281Z "Shapovalov, A. V." https://zbmath.org/authors/?q=ai:shapovalov.aleksandr-v Summary: The modified Fisher-Kolmogorov-Petrovskii-Piskunov equation with quasilocal quadratic competitive losses and variable coefficients in the small nonlocality parameter approximation is reduced to an equation with a nonlinear diffusion coefficient. Within the framework of a perturbation method, equations are obtained for the first terms of an asymptotic expansion of an approximate solution of the reduced equation. Particular solutions in separating variables are considered for the equations determining the first terms of the asymptotic series. The problem is reduced to an elliptic integral and one linear, homogeneous ordinary differential equation. Uniqueness of the solution of the inverse problem for a model of the dynamics of an age-structured population https://zbmath.org/1485.35427 2022-06-24T15:10:38.853281Z "Shcheglov, A. Yu." https://zbmath.org/authors/?q=ai:shcheglov.a-yu Summary: For the McKendrick model of the dynamics of an age-structured population, we consider the inverse problem of reconstructing two coefficients of the model: in the equation and in the nonlocal boundary condition of integral form. The values of the solution on a part of the boundary are used as the additional information in the inverse problem. We obtain conditions for the sought coefficients to be uniquely determined. The derived integral formulas can be used to solve the inverse problem numerically by the iteration method, taking into account the fact that the inverse problem is ill posed. Classification of the spreading behaviors of a two-species diffusion-competition system with free boundaries https://zbmath.org/1485.35432 2022-06-24T15:10:38.853281Z "Du, Yihong" https://zbmath.org/authors/?q=ai:du.yihong "Wu, Chang-Hong" https://zbmath.org/authors/?q=ai:wu.changhong Summary: In this paper, we revisit the spreading behavior of two invasive species modelled by a diffusion-competition system with two free boundaries in a radially symmetric setting, where the reaction terms depict a weak-strong competition scenario. Our previous work [the authors, ibid. 57, No. 2, Paper No. 52, 36 p. (2018; Zbl 1396.35028)] proves that from certain initial states, the two species develop into a chase-and-run coexistence'' state, namely the front of the weak species $$v$$ propagates at a fast speed and that of the strong species $$u$$ propagates at a slow speed, with their population masses largely segregated. Subsequent numerical simulations in [\textit{K. Khan} et al., J. Math. Biol. 83, No. 3, Paper No. 23, 43 p. (2021; Zbl 1477.35285)] suggest that for all possible initial states, only four different types of long-time dynamical behaviours can be observed: (1) chase-and-run coexistence, (2) vanishing of $$u$$ with $$v$$ spreading successfully, (3) vanishing of $$v$$ with $$u$$ spreading successfully, and (4) vanishing of both species. In this paper, we rigorously prove that, as the initial states vary, there are exactly five types of long-time dynamical behaviors: apart from the four mentioned above, there exists a fifth case, where both species spread successfully and their spreading fronts are kept within a finite distance to each other all the time. We conjecture that this new case can happen only when a parameter takes an exceptional value, which is why it has eluded the numerical observations of Khan et al. [loc. cit.]. A free boundary problem of some modified Leslie-gower predator-prey model with nonlocal diffusion term https://zbmath.org/1485.35435 2022-06-24T15:10:38.853281Z "Niu, Shiwen" https://zbmath.org/authors/?q=ai:niu.shiwen "Cheng, Hongmei" https://zbmath.org/authors/?q=ai:cheng.hongmei "Yuan, Rong" https://zbmath.org/authors/?q=ai:yuan.rong Summary: This paper is mainly considered a Leslie-Gower predator-prey model with nonlocal diffusion term and a free boundary condition. The model describes the evolution of the two species when they initially occupy the bounded region $$[0,h_0]$$. We first show that the problem has a unique solution defined for all $$t>0$$. Then, we establish the long-time dynamical behavior, including Spreading-vanishing dichotomy and Spreading-vanishing criteria. The dynamics of partially degenerate nonlocal diffusion systems with free boundaries https://zbmath.org/1485.35436 2022-06-24T15:10:38.853281Z "Zhang, Heting" https://zbmath.org/authors/?q=ai:zhang.heting "Li, Lei" https://zbmath.org/authors/?q=ai:li.lei.4|li.lei.3|li.lei.6|li.lei.5|li.lei.1|li.lei|li.lei.7|li.lei.2 "Wang, Mingxin" https://zbmath.org/authors/?q=ai:wang.mingxin|wang.mingxin.1 Summary: We consider a class of partially degenerate nonlocal diffusion systems with free boundaries. Such problems can describe the evolution of one species with nonlocal diffusion and the other without diffusion or with much slower diffusion. The existence, uniqueness, and regularity of global solutions are first proven. The criteria of spreading and vanishing are also established for the Lotka-Volterra type competition and prey-predator growth terms. Moreover, we investigate long-time behaviors of the solution and propose estimates of spreading speeds when spreading occurs. The dynamics of gonosomal evolution operators https://zbmath.org/1485.37073 2022-06-24T15:10:38.853281Z "Absalamov, Akmal T." https://zbmath.org/authors/?q=ai:absalamov.akmal-t "Rozikov, Utkir A." https://zbmath.org/authors/?q=ai:rozikov.utkir-a Summary: In this paper we investigate the dynamical systems generated by gonosomal evolution operator of sex linked inheritance depending on parameters. Mainly we study dynamical systems of a hemophilia which is biological group of disorders connected with genes that diminish the body's ability to control blood clotting or coagulation that is used to stop bleeding when a blood vessel is broken. For the gonosomal operator we discrebe all forms and give explicitly the types of fixed points. Moreover we study limit points of the trajectories of the corresponding dynamical system. Analysis of Caputo fractional-order model for COVID-19 with lockdown https://zbmath.org/1485.37074 2022-06-24T15:10:38.853281Z "Ahmed, Idris" https://zbmath.org/authors/?q=ai:ahmed.idris "Baba, Isa Abdullahi" https://zbmath.org/authors/?q=ai:baba.isa-abdullahi "Yusuf, Abdullahi" https://zbmath.org/authors/?q=ai:yusuf.abdullahi-a "Kumam, Poom" https://zbmath.org/authors/?q=ai:kumam.poom "Kumam, Wiyada" https://zbmath.org/authors/?q=ai:kumam.wiyada Summary: One of the control measures available that are believed to be the most reliable methods of curbing the spread of coronavirus at the moment if they were to be successfully applied is lockdown. In this paper a mathematical model of fractional order is constructed to study the significance of the lockdown in mitigating the virus spread. The model consists of a system of five nonlinear fractional-order differential equations in the Caputo sense. In addition, existence and uniqueness of solutions for the fractional-order coronavirus model under lockdown are examined via the well-known Schauder and Banach fixed theorems technique, and stability analysis in the context of Ulam-Hyers and generalized Ulam-Hyers criteria is discussed. The well-known and effective numerical scheme called fractional Euler method has been employed to analyze the approximate solution and dynamical behavior of the model under consideration. It is worth noting that, unlike many studies recently conducted, dimensional consistency has been taken into account during the fractionalization process of the classical model. A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative https://zbmath.org/1485.37075 2022-06-24T15:10:38.853281Z "Baleanu, Dumitru" https://zbmath.org/authors/?q=ai:baleanu.dumitru-i "Mohammadi, Hakimeh" https://zbmath.org/authors/?q=ai:mohammadi.hakimeh "Rezapour, Shahram" https://zbmath.org/authors/?q=ai:rezapour.shahram Summary: We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative. Bifurcation of periodic solutions of a delayed SEIR epidemic model with nonlinear incidence rate https://zbmath.org/1485.37076 2022-06-24T15:10:38.853281Z "Bernoussi, Amine" https://zbmath.org/authors/?q=ai:bernoussi.amine Summary: In this paper, we propose the SEIR epidemic model with delay and nonlinear incidence rate. The resulting model has two possible equilibria: if $$R_0 \leq 1$$, then the SEIR epidemic model has a disease-free equilibrium and if $$R_0>1$$, then the SEIR epidemic model admits a unique endemic equilibrium. By using suitable Lyapunov functionals and LaSalle's invariance principle, the global stability of a diseasefree equilibrium is established. Our main contribution affirms the existence of non constant periodic solutions which bifurcate from the endemic equilibrium when the delay crosses some critical values. Finally, some numerical simulations are presented to illustrate our theoretical results. Global dynamics of an SIRSI epidemic model with discrete delay and general incidence rate https://zbmath.org/1485.37077 2022-06-24T15:10:38.853281Z "Bernoussi, Amine" https://zbmath.org/authors/?q=ai:bernoussi.amine "Hattaf, Khalid" https://zbmath.org/authors/?q=ai:hattaf.khalid Summary: In this paper, we propose the global dynamics of an SIRSI epidemic model with discrete latent period and general nonlinear incidence function. By analyzing the corresponding characteristic equations, the local stability of the endemic equilibrium is established. By using suitable Lyapunov functionals and LaSalle's invariance principle, the global stability of the disease-free equilibrium and the endemic equilibrium are established for the SIRSI epidemic model with discrete latent period. Modelling and analysis of an one-predator two-prey ecological system with fear effect https://zbmath.org/1485.37078 2022-06-24T15:10:38.853281Z "Bhattacharyya, Anindita" https://zbmath.org/authors/?q=ai:bhattacharyya.anindita "Bose, Sanghita" https://zbmath.org/authors/?q=ai:bose.sanghita "Mondal, Ashok" https://zbmath.org/authors/?q=ai:mondal.ashok "Pal, A. K." https://zbmath.org/authors/?q=ai:pal.ashok-kumar|pal.arup-kumar|pal.anil-kumar|pal.asim-k|pal.amit-kumar|pal.ashis-kumar|pal.arun-kumar Summary: The present study deals with the dynamical response of a two-prey one predator model inculcating the anti-predator fear effect. The proposed model considers a Holling type II response function and it is intended to investigate the effect of the presence of fear among preys due to a predator. It is first shown that the system is bounded and the conditions of existence and stability of the equilibria of the proposed model have been furnished. Next the presence of Hopf bifurcation and limit cycles have been shown to explain the transition of the model from a stable to an unstable one. The study reveals that along with fear the interaction between the preys and predator can also be effectively stated as a control factor in determining dynamics of the model. The effect of anti-predator fear and mutual interaction between the preys and predator has been numerically simulated in order to potray the dynamics of the model and the occurrence of limit cycles. Mathematical modelling of the dynamics of human schistosomiasis with time-discrete delays https://zbmath.org/1485.37079 2022-06-24T15:10:38.853281Z "Eya, I. Ngningone" https://zbmath.org/authors/?q=ai:eya.i-ngningone "Yatat-Djeumen, I. V." https://zbmath.org/authors/?q=ai:yatat-djeumen.ivric-valaire "Etoua, R. M." https://zbmath.org/authors/?q=ai:etoua.remy-magloire "Tewa, J. J." https://zbmath.org/authors/?q=ai:tewa.jean-jules Summary: In this paper, we study a schistosomiasis model incorporating the miracidia and cercariae dynamics, discrete-time delays as well as control measures like water treatment. Modelling the dynamics of schistosomiasis infectious disease is quite challenging because of the different larval forms assumed by the parasite and the requirement of two hosts during the life cycle. Our model is generic in the sense that it considers both situations where particle depletion by hosts or snails could have or not a negligible impact on particle dynamics. Precisely, we introduce two parameters $$u$$ and $$v$$ such that when $$u=v=0$$, then particle depletion by hosts or snails is not considered; when $$u=v=1$$, then particle depletion by hosts and snails is considered. The model is analyzed to gain insights into the qualitative features of the disease-free equilibrium which allows the determination of the basic reproductive number $$\mathcal{R}_{u,v}$$. The Center Manifold Theory is used to discuss existence and local stability of an endemic equilibrium. Global sensitivity analysis (SA) of the schistosomiasis model and the basic reproduction number are carried out. SA results of the model point out the leading role of $$\eta$$, the parameter that shapes infection-induced death rate in humans, on the dynamics of humans (susceptible and infected), miracidia, cercariae and infected snails. They also reveal the pervasive role of $$\theta$$, the water treatment-induced death rate of snails, on the dynamics of infected humans, miracidia, snails (susceptible and infected) and cercariae. SA results of the basic reproduction number highlight the role of $$\eta,\theta,\lambda$$ (the contact rate of transmission of miracidia to susceptible snails), $$\varpi$$ (production rate of miracidia from feces of infected humans) and $$\gamma$$ (the transmission rate of cercariae to susceptible humans). Therefore, a possible way to control the disease could rely on the intensification of sanitization campaigns that will result in an increase of $$\theta$$ together with sensitization about the necessity to have a treatment once you are infected to reduce $$\eta$$. Solvability and stability of a fractional dynamical system of the growth of COVID-19 with approximate solution by fractional Chebyshev polynomials https://zbmath.org/1485.37080 2022-06-24T15:10:38.853281Z "Hadid, Samir B." https://zbmath.org/authors/?q=ai:hadid.samir-b "Ibrahim, Rabha W." https://zbmath.org/authors/?q=ai:ibrahim.rabha-waell "Altulea, Dania" https://zbmath.org/authors/?q=ai:altulea.dania "Momani, Shaher" https://zbmath.org/authors/?q=ai:momani.shaher-m Summary: Lately, many studies were offered to introduce the population dynamics of COVID-19. In this investigation, we extend different physical conditions of the growth by employing fractional calculus. We study a system of coupled differential equations, which describes the dynamics of the infection spreading between infected and asymptomatic styles. The healthy population properties are measured due to the social meeting. The result is associated with a macroscopic law for the population. This dynamic system is appropriate to describe the performance of growth rate of the infection and to verify if its control is appropriately employed. A unique solution, under self-mapping possessions, is investigated. Approximate solutions are presented by utilizing fractional integral of Chebyshev polynomials. Our methodology is based on the Atangana-Baleanu calculus, which provides various activity results in the simulation. We tested the suggested system by using live data. We found positive action in the graphs. Complex dynamics of a prey-predator system incorporating functional response dependent prey refuge with harvesting https://zbmath.org/1485.37081 2022-06-24T15:10:38.853281Z "Jana, Soovoojeet" https://zbmath.org/authors/?q=ai:jana.soovoojeet "Guria, Srabani" https://zbmath.org/authors/?q=ai:guria.srabani "Ghorai, Abhijit" https://zbmath.org/authors/?q=ai:ghorai.abhijit "Kar, Tapan Kumar" https://zbmath.org/authors/?q=ai:kar.tapan-kumar Summary: In this paper, we consider a prey-predator system allowing prey refuge and harvesting the prey species only. It is investigated under which condition the system has no limit cycle. An optimal harvesting policy is also formulated using Pontryagin's Maximum Principle. A comparison study have been done with the model in which the per individual prey refuge taken as constant. We investigate one and two parametric bifurcations thoroughly. Here we also discuss the bi-stability of the model in brief when the interior equilibrium is not unique. Some numerical simulations are given to verify our analytic works. Dynamics of a stochastic population model with Allee effects under regime switching https://zbmath.org/1485.37082 2022-06-24T15:10:38.853281Z "Ji, Weiming" https://zbmath.org/authors/?q=ai:ji.weiming "Liu, Meng" https://zbmath.org/authors/?q=ai:liu.meng Summary: A stochastic single-species model with Allee effects under regime switching is developed and detected in the present study. First, extinction and persistence of the model are dissected. Subsequently, sufficient criteria are offered to ensure that the model possesses a unique ergodic stationary distribution. Finally, the theoretical outcomes are employed to evaluate the evolution of the African wild dog (\textit{Lycaon pictus}) in Africa, and some significant functions of stochastic perturbations are exposed. On a family of Volterra cubic stochastic operators https://zbmath.org/1485.37083 2022-06-24T15:10:38.853281Z "Kurganov, K. A." https://zbmath.org/authors/?q=ai:kurganov.k-a "Jamilov, U. U." https://zbmath.org/authors/?q=ai:jamilov.uygun-u "Okhunova, M. O." https://zbmath.org/authors/?q=ai:okhunova.m-o Summary: In present paper we consider a family of discrete time Kolmogorov systems of three interaction population depending on a parameter $$\theta$$. We show that there is the critic value $$\theta^*$$ of parameter $$\theta$$ such that for $$\theta\in(\theta^*,1]$$ this evolution operator is a non-ergodic transformation and for $$\theta\in[0,\theta^*)$$ it has property being regular. We give some biological interpretations of our results. A stochastic eco-epidemiological system with patchy structure and transport-related infection https://zbmath.org/1485.37084 2022-06-24T15:10:38.853281Z "Ma, Zhihui" https://zbmath.org/authors/?q=ai:ma.zhihui "Han, Shuyan" https://zbmath.org/authors/?q=ai:han.shuyan "Li, Shenghua" https://zbmath.org/authors/?q=ai:li.shenghua Summary: In this paper, a stochastic eco-epidemiological system with patchy structure and transport-related infection is proposed and the stochastic dynamical behaviors are investigated. Firstly, by constructing suitable Lyapunov functions, it is revealed that there is a unique globally positive solution starting from the positive initial value. Secondly, it is proved that the presented system is stochastically ultimately bounded and the average in time of the second moment of solution is bounded. Thirdly, we prove that the large enough stochastic perturbations may lead the predator population and the diseases in the predator to be extinct while it is persistent in the deterministic system. Finally, some numerical simulations are given to test our theoretical results. Dynamical complexity in a tritrophic food chain model with prey harvesting https://zbmath.org/1485.37085 2022-06-24T15:10:38.853281Z "Sarkar, Krishnendu" https://zbmath.org/authors/?q=ai:sarkar.krishnendu "Ali, Nijamuddin" https://zbmath.org/authors/?q=ai:ali.nijamuddin "Guin, Lakshmi Narayan" https://zbmath.org/authors/?q=ai:guin.lakshmi-narayan Summary: The present investigation deals with a tritrophic food web model with Holling-Tanner type II functional response to clarify the dynamical complexity of the eco-systems in the natural environment. The objective of this study is to explore the harvesting mechanism scenario in a threedimensional interacting species system such as one prey and two specialist predators. Attention has been given to demonstrate the system characteristics near the biologically feasible equilibria. Specifically, stability, Hopf-Andronov bifurcation for the respective system parameters and dissipativeness has been performed in order to scrutinize the system behaviour. Lyapunov exponents are worked out numerically and an unstable scenario for significant parameters of the model system has been executed to characterize the complex dynamics. In addition to, we put forward a detailed numerical simulation to justify the chaotic dynamics of the present system. We conclude that chaotic dynamics can be executed by the prey harvesting parameters. Dynamics analysis for a discrete dynamic competition model https://zbmath.org/1485.37086 2022-06-24T15:10:38.853281Z "Yang, Xiuqin" https://zbmath.org/authors/?q=ai:yang.xiuqin "Liu, Feng" https://zbmath.org/authors/?q=ai:liu.feng.4 "Wang, Qingyi" https://zbmath.org/authors/?q=ai:wang.qingyi "Wang, Hua O." https://zbmath.org/authors/?q=ai:wang.hua-o Summary: In this paper, the dynamics of a discrete market share attraction model are investigated. It shows that the system can undergo flip bifurcation and chaos. The stability and bifurcation of a market share attraction model are analyzed by using the bifurcation theory and the center manifold theorem. The system displays complex dynamical behaviors, including period-1, 2, 4, 6, 8, 16 orbits, invariant cycle, a cascade of period-doubling, quasi-periodic orbits, and the chaotic sets. Numerical simulations illustrate the analysis and results. Dynamic of interactive model for information propagation across social networks media https://zbmath.org/1485.37090 2022-06-24T15:10:38.853281Z "Zhang, Yaming" https://zbmath.org/authors/?q=ai:zhang.yaming "Liu, Fei" https://zbmath.org/authors/?q=ai:liu.fei.2|liu.fei.1|liu.fei "Koura, Yaya H." https://zbmath.org/authors/?q=ai:koura.yaya-h "Wang, Hao" https://zbmath.org/authors/?q=ai:wang.hao.2|wang.hao.4|wang.hao.6|wang.hao.9|wang.hao.13|wang.hao.12|wang.hao.7|wang.hao.5|wang.hao.11|wang.hao.3|wang.hao.10|wang.hao.1 Summary: Controlling information diffusion or propagation through social networks can be challenging when dealing with information related to a subject of highest interest for the public. The complexity level of control depends on subject importance, users' dynamic, and network structure. When two published messages or pieces of information share the same interest for targeted readers, analyzing their propagation dynamic for control and prediction is of great interest. This article proposes to model, based on a modified interactive system with Holling-type functional response, the dynamic of underlying relationship between two broadcasted messages traveling through social networks media. We showed in the qualitative analysis of the proposed model that system could be stable at certain conditions, and the model-system exhibited very rich dynamical behavior. Numerical simulation results validated theoretical analyses and suggested adapting resources harvesting and assimilation efficiency for an authoritative message to stabilize the system and control the dissemination of information in a closed environment. Stability of traveling wavefronts for a 2D lattice dynamical system arising in a diffusive population model https://zbmath.org/1485.39016 2022-06-24T15:10:38.853281Z "Zhao, Haiqin" https://zbmath.org/authors/?q=ai:zhao.haiqin Summary: This paper is concerned with the traveling wavefronts of a 2D two-component lattice dynamical system. This problem arises in the modeling of a species with mobile and stationary subpopulations in an environment in which the habitat is two-dimensional and divided into countable niches. The existence and uniqueness of the traveling wavefronts of this system have been studied in [the author and \textit{S.-L. Wu}, Nonlinear Anal., Real World Appl. 12, No. 2, 1178--1191 (2011; Zbl 1243.34013)]. However, the stability of the traveling wavefronts remains unsolved. In this paper, we show that all noncritical traveling wavefronts with given direction of propagation and wave speed are exponentially stable in time. In particular, we obtain the exponential convergence rate. Application of control and optimal treatment for predator-prey model https://zbmath.org/1485.49005 2022-06-24T15:10:38.853281Z "Doust, M. H. Rahmani" https://zbmath.org/authors/?q=ai:doust.mohammad-hossein-rahmani "Shirazian, M." https://zbmath.org/authors/?q=ai:shirazian.mohammad "Shamsabadi, M." https://zbmath.org/authors/?q=ai:shamsabadi.mitra Summary: Mathematical ecology and mathematical epidemiology are major fields in both biology and applied mathematics. In the present paper, a fourdimensional eco-epidemiological model with infection in both prey and preda tor populations is studied. It consists of susceptible prey, infected prey, susceptible predator, and infected predator. The functional response is assumed to be of Lotka-Volterra type. The behavior of the system such as the existence, boundedness, and stability for solutions and equilibria are studied and also the basic reproduction number for the proposed model is computed. Moreover, a related control model and optimal treatment for the control model are presented. Finally, to verify the analytical discussion, a numerical simulation is carried out. Convergence of maximum likelihood supertree reconstruction https://zbmath.org/1485.62026 2022-06-24T15:10:38.853281Z "Dinh, Vu" https://zbmath.org/authors/?q=ai:dinh.vu "Ho, Lam Si Tung" https://zbmath.org/authors/?q=ai:ho.lam-si-tung Summary: Supertree methods are tree reconstruction techniques that combine several smaller gene trees (possibly on different sets of species) to build a larger species tree. The question of interest is whether the reconstructed supertree converges to the true species tree as the number of gene trees increases (that is, the consistency of supertree methods). In this paper, we are particularly interested in the convergence rate of the maximum likelihood supertree. Previous studies on the maximum likelihood supertree approach often formulate the question of interest as a discrete problem and focus on reconstructing the correct topology of the species tree. Aiming to reconstruct both the topology and the branch lengths of the species tree, we propose an analytic approach for analyzing the convergence of the maximum likelihood supertree method. Specifically, we consider each tree as one point of a metric space and prove that the distance between the maximum likelihood supertree and the species tree converges to zero at a polynomial rate under some mild conditions. We further verify these conditions for the popular exponential error model of gene trees. Modified Chebyshev collocation method for delayed predator-prey system https://zbmath.org/1485.65088 2022-06-24T15:10:38.853281Z "Dengata, J." https://zbmath.org/authors/?q=ai:dengata.j "Ma, Shufang" https://zbmath.org/authors/?q=ai:ma.shufang Summary: In this study, the approximate solutions of the predator-prey system with delay have been obtained by using the modified Chebyshev collocation method. The main technique is that this method transforms the original problem into a system of nonlinear algebraic equations. By using the residual function of the operator equations, error differential equations are constructed and thus the approximate solutions are corrected. A numerical example is given to confirm the reliability and applicability of the method, and comparisons with existing results are given. The numerical results show that the obtained solutions are in good agreement with earlier studies. Numerical analysis of high order time stepping schemes for a predator-prey system https://zbmath.org/1485.65103 2022-06-24T15:10:38.853281Z "Chrysafinos, Konstantinos" https://zbmath.org/authors/?q=ai:chrysafinos.konstantinos "Kostas, Dimitrios" https://zbmath.org/authors/?q=ai:kostas.dimitrios (no abstract) Hopf bifurcation of a delayed worm model with two latent periods https://zbmath.org/1485.68017 2022-06-24T15:10:38.853281Z "Liu, Juan" https://zbmath.org/authors/?q=ai:liu.juan "Zhang, Zizhen" https://zbmath.org/authors/?q=ai:zhang.zizhen Summary: We investigate a delayed epidemic model for the propagation of worm in wireless sensor network with two latent periods. We derive sufficient conditions for local stability of the worm-induced equilibrium of the system and the existence of Hopf bifurcation by regarding different combination of two latent time delays as the bifurcation parameter and analyzing the distribution of roots of the associated characteristic equation. In particular, we investigate the direction and stability of the Hopf bifurcation by means of the normal form theory and center manifold theorem. To verify analytical results, we present numerical simulations. Also, the effect of some influential parameters of sensor network is properly executed so that the oscillations can be reduced and removed from the network. Multi-interval pairwise compatibility graphs (extended abstract) https://zbmath.org/1485.68170 2022-06-24T15:10:38.853281Z "Ahmed, Shareef" https://zbmath.org/authors/?q=ai:ahmed.shareef "Rahman, Md. Saidur" https://zbmath.org/authors/?q=ai:rahman.md-saidur Summary: Let $$T$$ be an edge weighted tree and let $$d_{\min}$$, $$d_{\max}$$ be two non-negative real numbers where $$d_{\min}\leq d_{\max}$$. A pairwise compatibility graph (PCG) of $$T$$ for $$d_{\min}$$, $$d_{\max}$$ is a graph $$G$$ such that each vertex of $$G$$ corresponds to a distinct leaf of $$T$$ and two vertices are adjacent in $$G$$ if and only if the weighted distance between their corresponding leaves lies within the interval $$[d_{\min},d_{\max}]$$. A graph $$G$$ is a PCG if there exist an edge weighted tree $$T$$ and suitable $$d_{\min}$$, $$d_{\max}$$ such that $$G$$ is a PCG of $$T$$. Knowing that all graphs are not PCGs, in this paper we introduce a variant of pairwise compatibility graphs which we call multi-interval PCGs. A graph $$G$$ is a multi-interval PCG if there exist an edge weighted tree $$T$$ and some mutually exclusive intervals of nonnegative real numbers such that there is an edge between two vertices in $$G$$ if and only if the distance between their corresponding leaves in $$T$$ lies within any such intervals. If the number of intervals is $$k$$, then we call the graph a $$k$$-interval PCG. We show that every graph is a $$k$$-interval PCG for some $$k$$. We also prove that wheel graphs and a restricted subclass of series-parallel graphs are 2-interval PCGs. For the entire collection see [Zbl 1360.68012]. On the shortest common superstring of NGS reads https://zbmath.org/1485.68318 2022-06-24T15:10:38.853281Z "Braquelaire, Tristan" https://zbmath.org/authors/?q=ai:braquelaire.tristan "Gasparoux, Marie" https://zbmath.org/authors/?q=ai:gasparoux.marie "Raffinot, Mathieu" https://zbmath.org/authors/?q=ai:raffinot.mathieu "Uricaru, Raluca" https://zbmath.org/authors/?q=ai:uricaru.raluca Summary: The Shortest Superstring problem (SSP) consists, for a set of strings $$S = \{s_1,\cdots ,s_n\}$$ (with no $$s_i$$ substring of $$s_j$$), to find a minimum length string that contains all $$s_i$$, $$1\leq i \leq n$$, as substrings. This problem is proved to be NP-Complete and APX-hard. Guaranteed approximation algorithms have been proposed, the current best ratio being $$2\frac{11}{30}$$, which has been achieved through a long and difficult process. SSP is highly used in practice on next generation sequencing (NGS) data, which plays an increasingly important role in modern biological and medical research. In this note, we show that on NGS data the SSP approximation ratio reached by the classical algorithm of \textit{A. Blum} et al. [J. Assoc. Comput. Mach. 41, No. 4, 630--647 (1994; Zbl 0812.68075)], is usually below $$2\frac{11}{30}$$, while assuming specific characteristics of the data that are experimentally verified on a large sampling set. Moreover, we present an efficient linear time test for any input of strings of equal length, which allows to compute the approximation ratio that can be reached using the classical algorithm in [loc. cit.]. For the entire collection see [Zbl 1360.68012]. Solution of the problem of the deformation of a naturally twisted and extensible rod and its application to the investigation of conditions for the closure of DNA molecules https://zbmath.org/1485.74057 2022-06-24T15:10:38.853281Z "Ilyukhin, A. A." https://zbmath.org/authors/?q=ai:ilyukhin.aleksandr-alekseevich "Timoshenko, D. V." https://zbmath.org/authors/?q=ai:timoshenko.d-v (no abstract) Theory of elastic rods with rotational interaction of particles and its application to the investigation of conditions for the closure of DNA molecules https://zbmath.org/1485.74058 2022-06-24T15:10:38.853281Z "Ilyukhin, A. A." https://zbmath.org/authors/?q=ai:ilyukhin.aleksandr-alekseevich "Timoshenko, D. V." https://zbmath.org/authors/?q=ai:timoshenko.d-v (no abstract) Termination of the ice bucket challenge https://zbmath.org/1485.91040 2022-06-24T15:10:38.853281Z "Polyakov, Pavel" https://zbmath.org/authors/?q=ai:polyakov.pavel-y Summary: The ice bucket challenge is a social game aimed at encouraging donations to the amyotrophic lateral sclerosis association. The rules imply that each participant challenges each recruited follower to dump a bucket of ice water on his or her head. The network of who has nominated whom has a tree structure. The short duration of the ice bucket challenge is explained by using the reproduction number $$R_0$$, under the assumption that the capacity to recruit followers varies with the participant. The epidemic lasts until the interruption of the transmission tree occurring well before the depletion of susceptible followers. Such a tree is reconstructed from publicly available contact data and the interest in this game. Two competitive products diffusion in heterogeneous consumer social networks with repeat purchase https://zbmath.org/1485.91129 2022-06-24T15:10:38.853281Z "Huang, Qiwei" https://zbmath.org/authors/?q=ai:huang.qiwei "Zhang, Yulin" https://zbmath.org/authors/?q=ai:zhang.yulin.1 Summary: This paper studies the dynamics of two competitive products diffusion in heterogeneous consumer social networks with repeat purchase. We demonstrate a threshold for the diffusion rate above which a single product can persistently diffuse in heterogeneous consumer social networks without considering advertising strategy if the other product fails to diffuse, and there exists a unique positive equilibrium state where two competitive products coexist and persistently diffuse in heterogeneous consumer social networks without considering advertising strategy. We also prove that there exists at least one positive equilibrium state where two products coexist and persistently diffuse in heterogeneous consumer social networks if considering advertising strategy. The numerical simulations show that the higher the average degree of heterogeneous consumer social networks, the faster the two competitive products diffuse, and the shorter the time required to reach the stable state. Going viral: a gravity model of infectious diseases and tourism flows https://zbmath.org/1485.91164 2022-06-24T15:10:38.853281Z "Cevik, Serhan" https://zbmath.org/authors/?q=ai:cevik.serhan Summary: This paper develops an augmented gravity model framework to estimate the impact of infectious diseases on bilateral tourism flows among 38,184 pairs of countries over the period 1995--2017. The results confirm that international tourism is adversely affected by infectious disease risk, and the magnitude of this negative effect is statistically and economically significant. In the case of SARS, for example, a 10\% increase in the number of confirmed cases leads, on average, to a reduction of 4.7\% in international tourist arrivals. Furthermore, while infectious diseases appear to have a smaller and statistically insignificant negative effect on tourism flows to advanced economies, the magnitude and statistical significance of the impact of infectious diseases are much greater in developing countries, where such diseases tend to be more prevalent and health infrastructure lags behind. Entropy and free energy in structural biology. From thermodynamics to statistical mechanics to computer simulation https://zbmath.org/1485.92001 2022-06-24T15:10:38.853281Z "Meirovitch, Hagai" https://zbmath.org/authors/?q=ai:meirovitch.hagai Publisher's description: Computer simulation has become the main engine of development in statistical mechanics. In structural biology, computer simulation constitutes the main theoretical tool for structure determination of proteins and for calculation of the free energy of binding, which are important in drug design. Entropy and Free Energy in Structural Biology leads the reader to the simulation technology in a systematic way. The book, which is structured as a course, consists of four parts: Part I is a short course on probability theory emphasizing (1) the distinction between the notions of experimental probability, probability space, and the experimental probability on a computer, and (2) elaborating on the mathematical structure of product spaces. These concepts are essential for solving probability problems and devising simulation methods, in particular for calculating the entropy. Part II starts with a short review of classical thermodynamics from which a non-traditional derivation of statistical mechanics is devised. Theoretical aspects of statistical mechanics are reviewed extensively. Part III covers several topics in non-equilibrium thermodynamics and statistical mechanics close to equilibrium, such as Onsager relations, the two Fick's laws, and the Langevin and master equations. The Monte Carlo and molecular dynamics procedures are discussed as well. Part IV presents advanced simulation methods for polymers and protein systems, including techniques for conformational search and for calculating the potential of mean force and the chemical potential. Thermodynamic integration, methods for calculating the absolute entropy, and methodologies for calculating the absolute free energy of binding are evaluated. Enhanced by a number of solved problems and examples, this volume will be a valuable resource to advanced undergraduate and graduate students in chemistry, chemical engineering, biochemistry biophysics, pharmacology, and computational biology. The failures of mathematical anti-evolutionism https://zbmath.org/1485.92003 2022-06-24T15:10:38.853281Z "Rosenhouse, Jason" https://zbmath.org/authors/?q=ai:rosenhouse.jason Publisher's description: Anti-scientific misinformation has become a serious problem on many fronts, including vaccinations and climate change. One of these fronts is the persistence of anti-evolutionism, which has recently been given a superficially professional gloss in the form of the intelligent design movement. Far from solely being of interest to researchers in biology, anti-evolutionism must be recognized as part of a broader campaign with a conservative religious and political agenda. Much of the rhetorical effectiveness of anti-evolutionism comes from its reliance on seemingly precise mathematical arguments. This book, the first of its kind to be written by a mathematician, discusses and refutes these arguments. Along the way, it also clarifies common misconceptions about both biology and mathematics. Both lay audiences and professionals will find the book to be accessible and informative. On a nonlinear fractional order model of COVID-19 under AB-fractional derivative https://zbmath.org/1485.92004 2022-06-24T15:10:38.853281Z "Aydogan, Seher Melike" https://zbmath.org/authors/?q=ai:aydogan.seher-melike "Hussain, Azhar" https://zbmath.org/authors/?q=ai:hussain.azhar "Sakar, Fethiye Muge" https://zbmath.org/authors/?q=ai:sakar.fethiye-muge Summary: In this paper, we present a BOX mathematical model for the release of COVID-19.We intend to generalize the model to fractional order derivative in Atangana-Baleanu sense and to show the existence of solution for the fractional model using Schaefer's fixed point theorem and for the uniqueness of solution we make use of Banach fixed point theorem. By using Shehu transform and Picard successive iterative procedure, we explore the iterative solutions and its stability for the considered fractional model. Given the beginning of a new wave of COVID-19 spread in Indonesia, we present a numerical simulation to study and predict the spread of the disease in this country. Local lockdowns outperform global lockdown on the far side of the COVID-19 epidemic curve https://zbmath.org/1485.92005 2022-06-24T15:10:38.853281Z "Karatayev, Vadim A." https://zbmath.org/authors/?q=ai:karatayev.vadim-a "Anand, Madhur" https://zbmath.org/authors/?q=ai:anand.madhur "Bauch, Chris T." https://zbmath.org/authors/?q=ai:bauch.chris-t Summary: In the late stages of an epidemic, infections are often sporadic and geographically distributed. Spatially structured stochastic models can capture these important features of disease dynamics, thereby allowing a broader exploration of interventions. Here we develop a stochastic model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission among an interconnected group of population centers representing counties, municipalities, and districts (collectively, counties''). The model is parameterized with demographic, epidemiological, testing, and travel data from Ontario, Canada. We explore the effects of different control strategies after the epidemic curve has been flattened. We compare a local strategy of reopening (and reclosing, as needed) schools and workplaces county by county, according to triggers for county-specific infection prevalence, to a global strategy of province-wide reopening and reclosing, according to triggers for province-wide infection prevalence. For trigger levels that result in the same number of COVID-19 cases between the two strategies, the local strategy causes significantly fewer person-days of closure, even under high intercounty travel scenarios. However, both cases and person-days lost to closure rise when county triggers are not coordinated and when testing rates vary among counties. Finally, we show that local strategies can also do better in the early epidemic stage, but only if testing rates are high and the trigger prevalence is low. Our results suggest that pandemic planning for the far side of the COVID-19 epidemic curve should consider local strategies for reopening and reclosing. Preventing extinction in \textit{Rastrelliger brachysoma} using an impulsive mathematical model https://zbmath.org/1485.92006 2022-06-24T15:10:38.853281Z "Prathumwan, Din" https://zbmath.org/authors/?q=ai:prathumwan.din "Trachoo, Kamonchat" https://zbmath.org/authors/?q=ai:trachoo.kamonchat "Maiaugree, Wasan" https://zbmath.org/authors/?q=ai:maiaugree.wasan "Chaiya, Inthira" https://zbmath.org/authors/?q=ai:chaiya.inthira Summary: In this paper, we proposed a mathematical model of the population density of Indo-Pacific mackerel (Rastrelliger brachysoma) and the population density of small fishes based on the impulsive fishery. The model also considers the effects of the toxic environment that is the major problem in the water. The developed impulsive mathematical model was analyzed theoretically in terms of existence and uniqueness, positivity, and upper bound of the solution. The obtained solution has a periodic behavior that is suitable for the fishery. Moreover, the stability, permanence, and positive of the periodic solution are investigated. Then, we obtain the parameter conditions of the model for which Indo-Pacific mackerel conservation might be expected. Numerical results were also investigated to confirm our theoretical results. The results represent the periodic behavior of the population density of the Indo-Pacific mackerel and small fishes. The outcomes showed that the duration and quantity of fisheries were the keys to prevent the extinction of Indo-Pacific mackerel. A variational approach to morphogenesis: recovering spatial phenotypic features from epigenetic landscapes https://zbmath.org/1485.92019 2022-06-24T15:10:38.853281Z "Cortés-Poza, Yuriria" https://zbmath.org/authors/?q=ai:cortes-poza.yuriria "Padilla-Longoria, Pablo" https://zbmath.org/authors/?q=ai:padilla-longoria.pablo Summary: We model the process of cell fate determination of the flower \textit{Arabidopsis thaliana} employing a system of reaction-diffusion equations governed by a potential field. This potential field mimics the flower's epigenetic landscape as defined by Waddington. It is derived from the underlying genetic regulatory network (GRN), which is based on detailed experimental data obtained during cell fate determination in the early stages of development of the flower. The system of equations has a variational structure, and we use minimax techniques (in particular the Mountain Pass lemma) to show that the minimal energy solution of our functional is, in fact, the one that traverses the epigenetic landscape (the potential field) in the spatial order that corresponds to the correct architecture of the flower, that is, following the observed geometrical features of the meristem. This approach can generally be applied to systems with similar structures to establish a genotype to phenotype correspondence. From a broader perspective, this problem is related to phase transition models with a multiwell vector potential, and the results and methods presented here can potentially be applied in this case. Synchrony patterns in gene regulatory networks https://zbmath.org/1485.92045 2022-06-24T15:10:38.853281Z "Aguiar, Manuela A. D." https://zbmath.org/authors/?q=ai:aguiar.manuela-a-d "Dias, Ana P. S." https://zbmath.org/authors/?q=ai:dias.ana-paula-s "Ruan, Haibo" https://zbmath.org/authors/?q=ai:ruan.haibo Summary: Motivated by studying synchronization mechanisms in gene regulatory networks (GRNs) and their relation to evolutionary events such as genetic duplication and genetic redundancy, we consider two types of mathematical dynamical models of GRNs that depict general additive (SUM model) or multiplicative (MULT model) gene regulations. By a \textit{synchrony pattern} we mean clusters of synchronized genes whose states coincide for all time. The identification of the genes in each cluster of a network synchrony pattern results into (smaller) \textit{quotient network} equations representing the dynamical evolution of the original GRN equations restricted to that synchrony pattern. From the perspective of the dynamics of a GRN, in case the restricted dynamics functions as the regulatory core underlying the dynamics of the GRN, for example, if the synchrony pattern is globally attracting, the quotient network could represent a structural motif that performs a biological function, also known as a \textit{functional motif}. Gene duplication in GNRs has its analog in the \textit{lifting} process in the theory of coupled cell networks, which is the reverse of quotient: the unfolding of genes in a network, where each of those genes is unfolded into two or more genes, leads to a (bigger) \textit{lift network}. In general, there are many lifts associated with a fixed quotient network. In this paper, we obtain results on robust synchrony patterns for SUM and MULT dynamical models inspired by the existing theoretical results in the coupled cell network formalisms. Moreover, we explore the concepts of quotient network and network lifting in the context of GRNs which are related to the process of gene duplication and the phenomenon of subfunctionalization as an outcome of functional divergence. Dynamic analysis and optimal control for a model of hepatitis C with treatment https://zbmath.org/1485.92055 2022-06-24T15:10:38.853281Z "Zhang, Suxia" https://zbmath.org/authors/?q=ai:zhang.suxia "Xu, Xiaxia" https://zbmath.org/authors/?q=ai:xu.xiaxia Summary: A model for hepatitis C is formulated to study the effects of treatment and public concern on HCV transmission dynamics. The stability of equilibria and persistence of the model are analyzed, and an optimal control measure is performed to prevent the spread of HCV with minimal infected individuals and cost. The dynamical analysis reveals that the disease-free equilibrium of the model is asymptotically stable if the basic reproductive number $$\mathcal R_0$$ is less than unity. On the other hand, if $$\mathcal R_0 > 1,$$ the disease is uniformly persistent. Numerical simulations are conducted to investigate the influence of different vital parameters on $$\mathcal R_0$$. For the corresponding optimality system, the optimal solution is discussed by Pontryagin Maximum Principle, and the comparisons of model-predicted consequences with control or not are presented. Stability and Hopf bifurcation analysis of a delayed tobacco smoking model containing snuffing class https://zbmath.org/1485.92056 2022-06-24T15:10:38.853281Z "Zhang, Zizhen" https://zbmath.org/authors/?q=ai:zhang.zizhen "Zou, Junchen" https://zbmath.org/authors/?q=ai:zou.junchen "Upadhyay, Ranjit Kumar" https://zbmath.org/authors/?q=ai:kumar-upadhyay.ranjit "Pratap, A." https://zbmath.org/authors/?q=ai:pratap.ajay|pratap.amrit|pratap.anbalagan Summary: This paper is concerned with a delayed tobacco smoking model containing users in the form of snuffing. Its dynamics is studied in terms of local stability and Hopf bifurcation by regarding the time delay as a bifurcation parameter and analyzing the associated characteristic transcendental equation. Specially, specific formulas determining the stability and direction of the Hopf bifurcation are derived with the aid of the normal form theory and the center manifold theorem. Using LMI techniques, global exponential stability results for smoking present equilibrium have been presented. Computer simulations are implemented to explain the obtained analytical results. A stochastic model of HIV infection incorporating combined therapy of HAART driven by Lévy jumps https://zbmath.org/1485.92067 2022-06-24T15:10:38.853281Z "Cheng, Yan" https://zbmath.org/authors/?q=ai:cheng.yan "Zhang, Fumin" https://zbmath.org/authors/?q=ai:zhang.fumin "Zhao, Min" https://zbmath.org/authors/?q=ai:zhao.min Summary: A stochastic HIV infection model of virus-to-cell transmission is proposed, incorporating the antiretroviral drug therapy by introducing efficacy parameters of RTI and PI drugs, considering the Lévy noise for the inherent stochastic biochemical processes. First, we discuss the model existence of a global positive solution and, by applying Itô's formula, establish a sufficient condition for the extinction of infected CD $$4^+$$ T-cells and virus particles. Then, for proving the persistence in mean, a special method is investigated to handle the model. It is obtained that if $$\tilde{R}_1>1$$ the infected CD $$4^+$$ T-cells and virus particles will be persistent in mean. Finally, some numerical simulations are carried out to show the effects of inherent stochastic fluctuation. Stability of a general CTL-mediated immunity HIV infection model with silent infected cell-to-cell spread https://zbmath.org/1485.92068 2022-06-24T15:10:38.853281Z "Elaiw, A. M." https://zbmath.org/authors/?q=ai:elaiw.ahmed-m "AlShamrani, N. H." https://zbmath.org/authors/?q=ai:alshamrani.noura-h Summary: This paper proposes and analyzes a CTL-mediated HIV infection model. The model describes the interaction between healthy CD $$4^+$$ T cells, silent infected cells, active infected cells, free HIV particles, and cytotoxic T lymphocytes (CTLs). The healthy CD $$4^+$$ T cells can be infected when contacted by one of the following: (i) free HIV particles, (ii) silent infected cells, and (iii) active infected cells. The incidence rates of the healthy CD $$4^+$$ T cells with free HIV particles, silent infected cells, and active infected cells are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the incidence between the silent infected cells and healthy CD $$4^+$$ T cells. We first show that the model is well posed. The proposed model has three equilibria and their existence is governed by derived two threshold parameters: the basic HIV reproduction number $$\Re_0$$ and the HIV-specific CTL-mediated immunity reproduction number $$\Re_1$$. Under a set of conditions on the general functions and the parameters $$\Re_0$$ and $$\Re_1$$, we have proven the global asymptotic stability of all equilibria by using Lyapunov method. We have illustrated the theoretical results via numerical simulations. We have studied the effect of cell-to-cell (CTC) transmission on the dynamical behavior of the system. We have shown that inclusion of CTC transmission decreases the concentration of healthy CD $$4^+$$ T cells and increases the concentrations of infected cells and free HIV particles. Imperfect testing of individuals for infectious diseases: mathematical model and analysis https://zbmath.org/1485.92070 2022-06-24T15:10:38.853281Z "Villela, Daniel A. M." https://zbmath.org/authors/?q=ai:villela.daniel-a-m Summary: Testing symptomatic individuals for a disease permits health diagnostic units to effectively deliver treatment resources, if tests' results turn positive, which speeds up their treatment and might also decrease individuals' contacts to other ones. An imperfect test, however, might incorrectly consider susceptible individuals to be infected (false positives). In this case, testing reduces the epidemic in the expense of potentially misclassifying individuals. We present a mathematical model that describes the dynamics of imperfect testing and diagnostics for an infectious disease. Susceptible individuals turn to susceptible but deemed infected'' at a rate given by the test specificity. Infected individuals go to a state infected and tested positive'' at a rate given by the test sensitivity. Analysis of the model permits us to derive an expression for the basic reproduction number $$R_0$$ and to find the conditions for reaching $$R_0<1$$, in which case the disease-free equilibrium is stable. We also derive for a given sensitivity and specificity, the critical testing rate for reaching $$R_0<1$$. We also present numerical results to cover interesting scenarios such as applying different sensitivity and specificity values to obtain the basic reproduction number $$R_0<1$$. Finally, we devise a relative cost model to analyze the cost of testing rates. Causal inference in genetic trio studies https://zbmath.org/1485.92072 2022-06-24T15:10:38.853281Z "Bates, Stephen" https://zbmath.org/authors/?q=ai:bates.stephen "Sesia, Matteo" https://zbmath.org/authors/?q=ai:sesia.matteo "Candès, Emmanuel" https://zbmath.org/authors/?q=ai:candes.emmanuel-j Summary: We introduce a method to draw causal inferences -- inferences immune to all possible confounding -- from genetic data that include parents and offspring. Causal conclusions are possible with these data because the natural randomness in meiosis can be viewed as a high-dimensional randomized experiment. We make this observation actionable by developing a conditional independence test that identifies regions of the genome containing distinct causal variants. The proposed digital twin test compares an observed offspring to carefully constructed synthetic offspring from the same parents to determine statistical significance, and it can leverage any black-box multivariate model and additional nontrio genetic data to increase power. Crucially, our inferences are based only on a well-established mathematical model of recombination and make no assumptions about the relationship between the genotypes and phenotypes. We compare our method to the widely used transmission disequilibrium test and demonstrate enhanced power and localization. Nonreciprocity as a generic route to traveling states https://zbmath.org/1485.92073 2022-06-24T15:10:38.853281Z "You, Zhihong" https://zbmath.org/authors/?q=ai:you.zhihong "Baskaran, Aparna" https://zbmath.org/authors/?q=ai:baskaran.aparna "Marchetti, M. Cristina" https://zbmath.org/authors/?q=ai:marchetti.m-cristina Summary: We examine a nonreciprocally coupled dynamical model of a mixture of two diffusing species. We demonstrate that nonreciprocity, which is encoded in the model via antagonistic cross-diffusivities, provides a generic mechanism for the emergence of traveling patterns in purely diffusive systems with conservative dynamics. In the absence of nonreciprocity, the binary fluid mixture undergoes a phase transition from a homogeneous mixed state to a demixed state with spatially separated regions rich in one of the two components. Above a critical value of the parameter tuning nonreciprocity, the static demixed pattern acquires a finite velocity, resulting in a state that breaks both spatial and time-reversal symmetry, as well as the reflection parity of the static pattern. We elucidate the generic nature of the transition to traveling patterns using a minimal model that can be studied analytically. Our work has direct relevance to nonequilibrium assembly in mixtures of chemically interacting colloids that are known to exhibit nonreciprocal effective interactions, as well as to mixtures of active and passive agents where traveling states of the type predicted here have been observed in simulations. It also provides insight on transitions to traveling and oscillatory states seen in a broad range of nonreciprocal systems with nonconservative dynamics, from reaction--diffusion and prey--predators models to multispecies mixtures of microorganisms with antagonistic interactions. Asymptotic enumeration and distributional properties of galled networks https://zbmath.org/1485.92074 2022-06-24T15:10:38.853281Z "Fuchs, Michael" https://zbmath.org/authors/?q=ai:fuchs.michael "Yu, Guan-Ru" https://zbmath.org/authors/?q=ai:yu.guan-ru "Zhang, Louxin" https://zbmath.org/authors/?q=ai:zhang.louxin Summary: We show a first-order asymptotics result for the number of galled networks with $$n$$ leaves. This is the first class of phylogenetic networks of \textit{large} size for which an asymptotic counting result of such strength can be obtained. In addition, we also find the limiting distribution of the number of reticulation nodes of galled networks with $$n$$ leaves chosen uniformly at random. These results are obtained by performing an asymptotic analysis of a recent approach of \textit{A. D. M. Gunawan} et al. [Discrete Appl. Math. 283, 644--654 (2020; Zbl 1442.05093)] which was devised for the purpose of (exactly) counting galled networks. Moreover, an old result of \textit{E. A. Bender} and \textit{L. B. Richmond} [Discrete Math. 50, 135--141 (1984; Zbl 0553.05009)] plays a crucial role in our proofs, too. Spatial populations with seed-bank: well-posedness, duality and equilibrium https://zbmath.org/1485.92075 2022-06-24T15:10:38.853281Z "Greven, Andreas" https://zbmath.org/authors/?q=ai:greven.andreas "den Hollander, Frank" https://zbmath.org/authors/?q=ai:den-hollander.frank "Oomen, Margriet" https://zbmath.org/authors/?q=ai:oomen.margriet Summary: We consider a system of interacting Fisher-Wright diffusions with seed-bank. Individuals live in colonies and are subject to resampling and migration as long as they are \textit{active}. Each colony has a structured seed-bank into which individuals can retreat to become \textit{dormant}, suspending their resampling and migration until they become active again. As geographic space labeling the colonies we consider a countable abelian group $$\mathbb{G}$$ endowed with the discrete topology. The key example of interest is the Euclidean lattice $$\mathbb{G}=\mathbb{Z}^d, d\in \mathbb{N}$$. Our goal is to \textit{classify} the long-time behaviour of the system in terms of the underlying model parameters. In particular, we want to understand in what way the seed-bank enhances genetic diversity. We introduce three models of increasing generality, namely, individuals become dormant: (1) in the seed-bank of their colony; (2) in the seed-bank of their colony while adopting a \textit{random colour} that determines their wake-up time; (3) in the seed-bank of a \textit{random colony} while adopting a \textit{random colour}. The extension in (2) allows us to model wake-up times with fat tails while preserving the Markov property of the evolution. The extension in (3) allows us to place individuals in different colony when they become dormant. For each of the three models we show that the system of continuum stochastic differential equations, describing the population in the large-colony-size limit, has a unique strong solution. We also show that the system converges to a unique equilibrium depending on a single \textit{density parameter} that is determined by the initial state, and exhibits a dichotomy of \textit{coexistence} (= locally multi-type equilibrium) versus \textit{clustering} (= locally mono-type equilibrium) depending on the parameters controlling the migration and the seed-bank. The seed-bank slows down the loss of genetic diversity. In model (1), the dichotomy between clustering and coexistence is determined by migration only. In particular, clustering occurs for recurrent migration and coexistence occurs for transient migration, as for the system without seed-bank. In models (2) and (3), an interesting interplay between migration and seed-bank occurs. In particular, the dichotomy is affected by the seed-bank when the wake-up time has infinite mean. For instance, for \textit{critically recurrent migration} the system exhibits clustering for finite mean wake-up time and coexistence for infinite mean wake-up time. Hence, at the \textit{critical dimension} for the system without seed-bank, \textit{new universality classes} appear when the seed-bank is added. If the wake-up time has a sufficiently fat tail, then the seed-bank determines the dichotomy and migration has no effect at all. The presence of the seed-bank makes the proof of convergence to a unique equilibrium a conceptually delicate issue. By combining duality arguments with coupling techniques, we show that our results also hold when we replace the Fisher-Wright diffusion function by a more general diffusion function, drawn from an appropriate class. Distance metrics for ranked evolutionary trees https://zbmath.org/1485.92076 2022-06-24T15:10:38.853281Z "Kim, Jaehee" https://zbmath.org/authors/?q=ai:kim.jaehee-h "Rosenberg, Noah A." https://zbmath.org/authors/?q=ai:rosenberg.noah-a "Palacios, Julia A." https://zbmath.org/authors/?q=ai:palacios.julia-a Summary: Genealogical tree modeling is essential for estimating evolutionary parameters in population genetics and phylogenetics. Recent mathematical results concerning ranked genealogies without leaf labels unlock opportunities in the analysis of evolutionary trees. In particular, comparisons between ranked genealogies facilitate the study of evolutionary processes of different organisms sampled at multiple time periods. We propose metrics on ranked tree shapes and ranked genealogies for lineages isochronously and heterochronously sampled. Our proposed tree metrics make it possible to conduct statistical analyses of ranked tree shapes and timed ranked tree shapes or ranked genealogies. Such analyses allow us to assess differences in tree distributions, quantify estimation uncertainty, and summarize tree distributions. We show the utility of our metrics via simulations and an application in infectious diseases. A novel algorithm for constructing rooted phylogenetic trees based on rooted triplets https://zbmath.org/1485.92077 2022-06-24T15:10:38.853281Z "Poormohammadi, Hadi" https://zbmath.org/authors/?q=ai:poormohammadi.hadi "Zarchi, Mohsen Sardari" https://zbmath.org/authors/?q=ai:zarchi.mohsen-sardari "Sehati, Mohamad Ali" https://zbmath.org/authors/?q=ai:sehati.mohamad-ali "Mirabi, Mohamad" https://zbmath.org/authors/?q=ai:mirabi.mohamad "Zarch, Seyaed Hasan Mortazavi" https://zbmath.org/authors/?q=ai:zarch.seyaed-hasan-mortazavi (no abstract) Switching systems with dwell time: computing the maximal Lyapunov exponent https://zbmath.org/1485.92078 2022-06-24T15:10:38.853281Z "Chitour, Yacine" https://zbmath.org/authors/?q=ai:chitour.yacine "Guglielmi, Nicola" https://zbmath.org/authors/?q=ai:guglielmi.nicola "Protasov, Vladimir Yu." https://zbmath.org/authors/?q=ai:protasov.vladimir-yu "Sigalotti, Mario" https://zbmath.org/authors/?q=ai:sigalotti.mario Summary: We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete-continuous) linear switching systems on graphs, in which some modes correspond to discrete actions and some others correspond to continuous-time evolutions. Each discrete action has its own positive weight which accounts for its time-duration. We develop a theory of stability for the mixed systems; in particular, we prove the existence of an invariant Lyapunov norm for mixed systems on graphs and study its structure in various cases, including discrete-time systems for which discrete actions have inhomogeneous time durations. This allows us to adapt recent methods for the joint spectral radius computation (Gripenberg's algorithm and the invariant polytope algorithm) to compute the Lyapunov exponent of mixed systems on graphs. Dynamics of a class of host-parasitoid models with external stocking upon parasitoids https://zbmath.org/1485.92079 2022-06-24T15:10:38.853281Z "Bektešević, Jasmin" https://zbmath.org/authors/?q=ai:bektesevic.jasmin "Hadžiabdić, Vahidin" https://zbmath.org/authors/?q=ai:hadziabdic.vahidin "Kalabušić, Senada" https://zbmath.org/authors/?q=ai:kalabusic.senada "Mehuljić, Midhat" https://zbmath.org/authors/?q=ai:mehuljic.midhat "Pilav, Esmir" https://zbmath.org/authors/?q=ai:pilav.esmir Summary: This paper is motivated by the series of research papers that consider parasitoids' external input upon the host-parasitoid interactions. We explore a class of host-parasitoid models with variable release and constant release of parasitoids. We assume that the host population has a constant rate of increase, but we do not assume any density dependence regulation other than parasitism acting on the host population. We compare the obtained results for constant stocking with the results for proportional stocking. We observe that under a specific condition, the release of a constant number of parasitoids can eventually drive the host population (pests) to extinction. There is always a boundary equilibrium where the host population extinct occurs, and the parasitoid population is stabilized at the constant stocking level. The constant and variable stocking can decrease the host population level in the unique interior equilibrium point; on the other hand, the parasitoid population level stays constant and does not depend on stocking. We prove the existence of Neimark-Sacker bifurcation and compute the approximation of the closed invariant curve. Then we consider a few host-parasitoid models with proportional and constant stocking, where we choose well-known probability functions of parasitism. By using the software package Mathematica we provide numerical simulations to support our study. A way to model stochastic perturbations in population dynamics models with bounded realizations https://zbmath.org/1485.92080 2022-06-24T15:10:38.853281Z "Caraballo, Tomás" https://zbmath.org/authors/?q=ai:caraballo.tomas "Colucci, Renato" https://zbmath.org/authors/?q=ai:colucci.renato "López-de-la-Cruz, Javier" https://zbmath.org/authors/?q=ai:lopez-de-la-cruz.javier "Rapaport, Alain" https://zbmath.org/authors/?q=ai:rapaport.alain In this paper, the authors adopt the Ornstein-Uhlenbeck process to discuss model dynamical systems subjected to bounded noisy perturbations. By with the help of some basic models in population dynamics such as the logistic equations and competitive Lotka-Volterra systems, they describe the main characteristics of this new approach. Moreover, to illustrate the advantages of this new approach, some numerical experiments are provide to examine the theoretical results. Reviewer: Shi-Liang Wu (Xi'an) Hopf bifurcation and chaos control for a Leslie-Gower type generalist predator model https://zbmath.org/1485.92081 2022-06-24T15:10:38.853281Z "Chen, Qin" https://zbmath.org/authors/?q=ai:chen.qin "Gao, Jianguo" https://zbmath.org/authors/?q=ai:gao.jianguo Summary: This paper is concerned with chaos control and bifurcations of the Leslie-Gower-type generalist predator model in a tri-trophic food web system with the time-delayed feedback control. First, the distribution of the roots of the related characteristic equations is analyzed by the polynomial theorem, the conditions to guarantee the existence of Hopf bifurcation are given by choosing the time delay as a bifurcation parameter. Then, the explicit formula for direction of Hopf bifurcation and stability of periodic solutions bifurcating are determined by using the normal form theory and center manifold theorem. Finally, the correctness of our theoretical analysis is verified by some numerical simulation. Dynamics of a stochastic phytoplankton-toxin phytoplankton-zooplankton model https://zbmath.org/1485.92082 2022-06-24T15:10:38.853281Z "Chen, Zhewen" https://zbmath.org/authors/?q=ai:chen.zhewen "Zhang, Shuwen" https://zbmath.org/authors/?q=ai:zhang.shuwen "Wei, Chunjin" https://zbmath.org/authors/?q=ai:wei.chunjin Summary: Environmental fluctuations and toxin-producing phytoplankton are crucial factors affecting marine ecosystems. In this paper, we propose a stochastic phytoplankton-toxin phytoplankton-zooplankton model to study the effect of environmental fluctuations on extinction and persistence of the population. The results show that large environmental fluctuations may lead to the extinction of the population, and small environmental fluctuation can keep population weakly persistent in the mean. We also find that the noise-induced extinction of one phytoplankton population may lead to the density increase of the other phytoplankton population in two competitive phytoplankton populations. By constructing appropriate Lyapunov functions, we obtain the sufficient conditions for the existence of an ergodic stationary distribution of the model. Finally, numerical simulations are carried out to support our main results. $$\Lambda$$-coalescents arising in a population with dormancy https://zbmath.org/1485.92083 2022-06-24T15:10:38.853281Z "Cordero, Fernando" https://zbmath.org/authors/?q=ai:cordero.fernando "Casanova, Adrián González" https://zbmath.org/authors/?q=ai:casanova.adrian-gonzalez "Schweinsberg, Jason" https://zbmath.org/authors/?q=ai:schweinsberg.jason-ross "Wilke-Berenguer, Maite" https://zbmath.org/authors/?q=ai:wilke-berenguer.maite Summary: Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with $$N$$ dormant individuals waking up independently of each other according to a given distribution. Once an individual is awake, it starts reproducing at a constant rate. By the end of spring, all individuals are awake and continue reproducing independently as Yule processes during the whole summer. In the winter, $$N$$ individuals chosen uniformly at random go to sleep until the next spring, and the other individuals die. We show that because an individual that wakes up unusually early can have a large number of surviving descendants, for some choices of model parameters the genealogy of the population will be described by a $$\Lambda$$-coalescent. In particular, the beta coalescent can describe the genealogy when the rate at which individuals wake up increases exponentially over time. We also characterize the set of all $$\Lambda$$-coalescents that can arise in this framework. Dynamic behaviors of Lotka-Volterra predator-prey model incorporating predator cannibalism https://zbmath.org/1485.92084 2022-06-24T15:10:38.853281Z "Deng, Hang" https://zbmath.org/authors/?q=ai:deng.hang "Chen, Fengde" https://zbmath.org/authors/?q=ai:chen.fengde "Zhu, Zhenliang" https://zbmath.org/authors/?q=ai:zhu.zhenliang "Li, Zhong" https://zbmath.org/authors/?q=ai:li.zhong Summary: A Lotka-Volterra predator-prey model incorporating predator cannibalism is proposed and studied in this paper. The existence and stability of all possible equilibria of the system are investigated. Our study shows that cannibalism has both positive and negative effect on the stability of the system, it depends on the dynamic behaviors of the original system. If the predator species in the system without cannibalism is extinct, then suitable cannibalism may lead to the coexistence of both species, in this case, cannibalism stabilizes the system. If the cannibalism rate is large enough, the prey species maybe driven to extinction, while the predator species are permanent. If the two species coexist in the stable state in the original system, then predator cannibalism may lead to the extinction of the prey species. In this case, cannibalism has an unstable effect. Numeric simulations support our findings. The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative https://zbmath.org/1485.92085 2022-06-24T15:10:38.853281Z "Djilali, Salih" https://zbmath.org/authors/?q=ai:djilali.salih "Ghanbari, Behzad" https://zbmath.org/authors/?q=ai:ghanbari.behzad Summary: In this research, we discuss the influence of an infectious disease in the evolution of ecological species. A computational predator-prey model of fractional order is considered. Also, we assume that there is a non-fatal infectious disease developed in the prey population. Indeed, it is considered that the predators have a cooperative hunting. This situation occurs when a pair or group of animals coordinate their activities as part of their hunting behavior in order to improve their chances of making a kill and feeding. In this model, we then shift the role of standard derivatives to fractional-order derivatives to take advantage of the valuable benefits of this class of derivatives. Moreover, the stability of equilibrium points is studied. The influence of this infection measured by the transmission rate on the evolution of predator-prey interaction is determined. Many scenarios are obtained, which implies the richness of the suggested model and the importance of this study. The graphical representation of the mathematical results is provided through a precise numerical scheme. This technique enables us to approximate other related models including fractional-derivative operators with high accuracy and efficiency. Stability analysis of discrete-time multi-patch Beddington-DeAngelis type predator-prey model with time-varying delay https://zbmath.org/1485.92086 2022-06-24T15:10:38.853281Z "Feng, Jiqiang" https://zbmath.org/authors/?q=ai:feng.jiqiang "Zhao, Zhiqiang" https://zbmath.org/authors/?q=ai:zhao.zhiqiang Summary: This paper is concerned with the stability of a discrete-time multi-patch Beddington-DeAngelis-type predator-prey model with time-varying delay, where the dispersal of both predators and prey is considered. A nonstandard finite difference scheme is used to discretize this model. Then, combining the Lyapunov-Krasovskii method with the graph-theoretical technique, a stability criterion is derived, which is closely related to the dispersal topology. And an example with numerical simulation is given to demonstrate the effectiveness of the obtained results. Evolutionarily stable strategies in stable and periodically fluctuating populations: the Rosenzweig-MacArthur predator-prey model https://zbmath.org/1485.92087 2022-06-24T15:10:38.853281Z "Grunert, Katrin" https://zbmath.org/authors/?q=ai:grunert.katrin "Holden, Helge" https://zbmath.org/authors/?q=ai:holden.helge "Stenseth, Nils Chr." https://zbmath.org/authors/?q=ai:stenseth.nils-chr (no abstract) Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments https://zbmath.org/1485.92088 2022-06-24T15:10:38.853281Z "He, Xin" https://zbmath.org/authors/?q=ai:he.xin "Zhao, Xin" https://zbmath.org/authors/?q=ai:zhao.xin "Feng, Tao" https://zbmath.org/authors/?q=ai:feng.tao "Qiu, Zhipeng" https://zbmath.org/authors/?q=ai:qiu.zhipeng In this paper, based on the deterministic prey-predator model owning foraging arena scheme, the authors have proposed a stochastic foraging arena prey-predator model in presence of environmental pollution. The sufficient criterions for uniform weak persistence in the mean and extinction have been obtained. The threshold between persistence and extinction has been also derived for the prey population. The authors have also showed the existence of a positive periodic solution under appropriate conditions. Finally, the authors present some numerical simulations to visually demonstrate their theoretical results. This paper is mostly inspired by the works of \textit{M. Liu} and \textit{K. Wang} [Survival analysis of stochastic single-species population models in polluted environments'', Ecol. Model. 220, No. 9--10, 1347--1357 (2009; \url{doi:10.1016/j.ecolmodel.2009.03.001})]. Reviewer: Yingxin Guo (Qufu) A stochastic predator-prey model for integrated pest management https://zbmath.org/1485.92089 2022-06-24T15:10:38.853281Z "Huang, Lidong" https://zbmath.org/authors/?q=ai:huang.lidong "Chen, Xingshu" https://zbmath.org/authors/?q=ai:chen.xingshu "Tan, Xuewen" https://zbmath.org/authors/?q=ai:tan.xuewen "Chen, Xiaochou" https://zbmath.org/authors/?q=ai:chen.xiaochou "Liu, Xinzhi" https://zbmath.org/authors/?q=ai:liu.xinzhi Summary: This paper studies a stochastic predator-prey model for integrated pest management. It shows that the system has a positive solution that exists globally. The long time behavior of the system is investigated, and a condition for the pest to go extinct is given. Then the numerical simulations are carried out to illustrate our theoretical results and facilitate their interpretation. Predator-prey pattern formation driven by population diffusion based on Moore neighborhood structure https://zbmath.org/1485.92090 2022-06-24T15:10:38.853281Z "Huang, Tousheng" https://zbmath.org/authors/?q=ai:huang.tousheng "Zhang, Huayong" https://zbmath.org/authors/?q=ai:zhang.huayong "Hu, Zhengran" https://zbmath.org/authors/?q=ai:hu.zhengran "Pan, Ge" https://zbmath.org/authors/?q=ai:pan.ge "Ma, Shengnan" https://zbmath.org/authors/?q=ai:ma.shengnan "Zhang, Xiumin" https://zbmath.org/authors/?q=ai:zhang.xiumin "Gao, Zichun" https://zbmath.org/authors/?q=ai:gao.zichun Summary: Diffusion-driven instability is a basic nonlinear mechanism for pattern formation. Therefore, the way of population diffusion may play a determinative role in the spatiotemporal dynamics of biological systems. In this research, we launch an investigation on the pattern formation of a discrete predator-prey system where the population diffusion is based on the Moore neighborhood structure instead of the von Neumann neighborhood structure widely applied previously. Under pattern formation conditions which are determined by Turing instability analysis, numerical simulations are performed to reveal the spatiotemporal complexity of the system. A pure Turing instability can induce the self-organization of many basic types of patterns as described in the literature, as well as new spiral-spot and labyrinth patterns which show the temporally oscillating and chaotic property. Neimark-Sacker-Turing and flip-Turing instability can lead to the formation of circle, spiral and much more complex patterns, which are self-organized via spatial symmetry breaking on the states that are homogeneous in space and non-periodic in time. Especially, the emergence of spiral pattern suggests that spatial order can generate from temporal disorder, implying that even when the predator-prey dynamics in one site is chaotic, the spatially global dynamics may still be predictable. The results obtained in this research suggest that when the way of population diffusion changes, the pattern formation in the predator-prey systems demonstrates great differences. This may provide realistic significance to explain more general predator-prey coexistence. Modeling the Allee effect and fear effect in predator-prey system incorporating a prey refuge https://zbmath.org/1485.92091 2022-06-24T15:10:38.853281Z "Huang, Ying" https://zbmath.org/authors/?q=ai:huang.ying "Zhu, Zhenliang" https://zbmath.org/authors/?q=ai:zhu.zhenliang "Li, Zhong" https://zbmath.org/authors/?q=ai:li.zhong Summary: In this paper, we consider a predator-prey model with Allee effect, fear effect and prey refuge. By considering the prey refuge as a parameter, we give the threshold condition for the stability of the system, and prove that the system undergoes a supercritical Hopf bifurcation. We show that increasing the prey refuge or Allee effect can make the dynamical behavior of the system more complicated; the fear effect or Allee effect has no influence on the prey density, but can lead to a decrease of the predator population at positive equilibrium. A delay differential equation model of mealybugs and Green lacewings https://zbmath.org/1485.92092 2022-06-24T15:10:38.853281Z "Jankaew, Kittipol" https://zbmath.org/authors/?q=ai:jankaew.kittipol "Rattanakul, Chontita" https://zbmath.org/authors/?q=ai:rattanakul.chontita "Sarika, Warunee" https://zbmath.org/authors/?q=ai:sarika.warunee Summary: In this paper, we propose and analyze a mathematical model of mealybugs and green lacewings with time delay to investigate the population dynamics of mealybugs (a major insect pest of cassava) and green lacewings (a natural enemy of mealybugs) when the time delay in the development of green lacewings is taken in to account. Hopf bifurcation theorem and Routh-Hurwitz criteria are utilized so that the conditions on the model parameters which differentiate various dynamic behaviors of the model are obtained. Computer simulations are also carried out to illustrate our theoretical predictions. Chaotic behavior observed in the field data is also investigated numerically. Bifurcations and hybrid control in a $$3 \times 3$$ discrete-time predator-prey model https://zbmath.org/1485.92093 2022-06-24T15:10:38.853281Z "Khan, Abdul Qadeer" https://zbmath.org/authors/?q=ai:khan.abdul-qadeer "Kiyani, Azhar Zafar" https://zbmath.org/authors/?q=ai:kiyani.azhar-zafar "Ahmad, Imtiaz" https://zbmath.org/authors/?q=ai:ahmad.imtiaz The authors are concerned with the analysis of a discrete model describing the dynamics of one predator and two prey populations suggested by \textit{M. R. Sagaya Raj} et al. [Dynamical behavior in a three species discrete model of prey-predator interactions'', Int. J. Comput. Sci. Math. 5, 11--20 (2013)], $x_{n+1}=\left( 1+a\right) x_{n}-bx_{n}z_{n},\quad y_{n+1}=ry_{n}\left( 1-y_{n}\right) -cy_{n}z_{n},\quad z_{n+1}=\left( 1-d\right) z_{n} +ex_{n}z_{n}+fy_{n}z_{n}.$ In the cited paper, five equilibria of this system, \begin{align*} E_{0} & =\left( 0,0,0\right) ,\qquad E_{1}=\left( 0,\frac{r-1} {r},0\right) ,\qquad E_{2}=\left( 0,\frac{d}{f},\frac{rf-f-dr}{cf}\right) ,\\ E_{3} & =\left( \frac{d}{e},\frac{r-1}{r},0\right) ,\qquad E_{4}=\left( \frac{br\left( d-f\right) +f\left( b+ac\right) }{ber},\frac{br-b-ac} {br},\frac{a}{b}\right) , \end{align*} were found and the first three were classified with respect to their stability. Relevant details were provided and supported with numerical simulations. The authors of the paper under review argued that Sagaya Raj et al. cannot give complete local dynamical classifications to interested readers, which is still further consideration and improvements towards local dynamical properties along with topological classifications and bifurcation analysis for the model under consideration''. \ Complementing the results in the cited paper, they revisited stability properties of all five equilibria. Surprisingly, not all characterizations of the equilibria in Lemmas 4.1 and 4.2 agree with those reported by Sagaya Raj et al. Lemma 4.1 characterizes the equilibrium $$E_{0}$$ similarly to Proposition 2 in the cited paper except for the claim that $$E_{0}$$ cannot be a sink, contrary to the statement that $$E_{0}$$ is a sink if $$r<1,$$ $$-2<a<0,$$ and $$0<d<2$$ in the latter result. Likewise, Lemma 4.2 claims that $$E_{1}$$ is never sink'', contrary to Proposition 3 proved by Sagaya Raj et al.\ Unfortunately, neither explanations nor the proofs are provided for both lemmas. Lemmas 4.3 - 4.6 complement the classification in the cited paper, still without proofs. Proposition 4 characterizes $$E_{2}$$ as a sink, source or saddle for different combinations of parameters whereas Lemma 4.3 refers to stable or unstable nodes, saddle nodes, or non-hyperbolic points. The equilibrium $$E_{3}$$ is classified in Lemma 4.4 as a stable or unstable focus-node or a saddle focus node and $$E_{4}$$ is claimed to be a sink in Lemma 4.5; both results lack proofs. The authors go on discussing further properties of equilibria including periodicity (Section 5, proofs of Theorems 5.1 and 5.2 are sketched), bifurcations (Sections 6 and 7, some explanations are provided in the latter one). Numerical simulations are considered in Section 8 and hybrid control of bifurcations is the subject of Section 9. Conclusions and further work are discussed in the final Section 10. Lack of details makes the comprehension of the results challenging. Reviewer: Svitlana P. Rogovchenko (Kristiansand) Impact of Michaelis-Menten type harvesting in a Lotka-Volterra predator-prey system incorporating fear effect https://zbmath.org/1485.92094 2022-06-24T15:10:38.853281Z "Lai, Liyun" https://zbmath.org/authors/?q=ai:lai.liyun "Yu, Xiangqin" https://zbmath.org/authors/?q=ai:yu.xiangqin "He, Mengxin" https://zbmath.org/authors/?q=ai:he.mengxin "Li, Zhong" https://zbmath.org/authors/?q=ai:li.zhong Summary: We propose and study a Lotka-Volterra predator-prey system incorporating both Michaelis-Menten-type prey harvesting and fear effect. By qualitative analysis of the eigenvalues of the Jacobian matrix we study the stability of equilibrium states. By applying the differential inequality theory we obtain sufficient conditions that ensure the global attractivity of the trivial equilibrium. By applying Dulac criterion we obtain sufficient conditions that ensure the global asymptotic stability of the positive equilibrium. Our study indicates that the catchability coefficient plays a crucial role on the dynamic behavior of the system; for example, the catchability coefficient is the Hopf bifurcation parameter. Furthermore, for our model in which harvesting is of Michaelis-Menten-type, the catchability coefficient is within a certain range; increasing the capture rate does not change the final number of prey population, but reduces the predator population. Meanwhile, the fear effect of the prey species has no influence on the dynamic behavior of the system, but it can affect the time when the number of prey species reaches stability. Numeric simulations support our findings. Fractional modeling and control in a delayed predator-prey system: extended feedback scheme https://zbmath.org/1485.92095 2022-06-24T15:10:38.853281Z "Li, Shuai" https://zbmath.org/authors/?q=ai:li.shuai "Huang, Chengdai" https://zbmath.org/authors/?q=ai:huang.chengdai "Guo, Shuli" https://zbmath.org/authors/?q=ai:guo.shuli "Song, Xinyu" https://zbmath.org/authors/?q=ai:song.xinyu Summary: This paper's goal is to delve into the fractional modeling and bifurcation control for a predator-prey model with prey dispersal and gestation delay. First, the bifurcation criteria for the uncontrolled system are obtained by viewing gestation delay as a bifurcation parameter. It is revealed that gestation delay can induce periodic oscillations. Then, an extended feedback controller is deeply conceived to suppress Hopf bifurcation for the underlying system. The results reflect that the stability behaviors of the uncontrolled system are saliently enhanced by adjusting feedback gain and feedback delay if other coefficients are fixed. To protrude the correctness and excellent feature of our works, two simulation examples are eventually carried out. Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps https://zbmath.org/1485.92096 2022-06-24T15:10:38.853281Z "Li, Wenrui" https://zbmath.org/authors/?q=ai:li.wenrui "Zhang, Qimin" https://zbmath.org/authors/?q=ai:zhang.qimin "Anke, Meyer-Baese" https://zbmath.org/authors/?q=ai:anke.meyer-baese "Ye, Ming" https://zbmath.org/authors/?q=ai:ye.ming "Li, Yan" https://zbmath.org/authors/?q=ai:li.yan.4|li.yan.2|li.yan.1|li.yan.6|li.yan|li.yan.5|li.yan.10|li.yan.3|li.yan.9|li.yan.8|li.yan.7 A Taylor approximation scheme for a class of age-dependent stochastic age-dependent population equations with mean-reverting Ornstein-Uhlenbeck (OU) process and Poisson jumps is presented, new numerical approximation is developed to investigate the properties of this stochastic age-dependent population systems. In case that the coefficients of drift and diffusion are Taylor approximations, it was proved that the numerical solutions converge to the exact solutions for these equations, the convergence order of the numerical scheme and numerical simulations are also given. Reviewer: Shengqiang Liu (Harbin) Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response https://zbmath.org/1485.92097 2022-06-24T15:10:38.853281Z "Mortuja, Md Golam" https://zbmath.org/authors/?q=ai:mortuja.md-golam "Chaube, Mithilesh Kumar" https://zbmath.org/authors/?q=ai:chaube.mithilesh-kumar "Kumar, Santosh" https://zbmath.org/authors/?q=ai:kumar.santosh.2|kumar.santosh.3|kumar.santosh.1|kumar.santosh.4|kumar.santosh Summary: In this work, the dynamics of a predator-prey system considering square root type functional response for prey herd behaviour and nonlinear prey harvesting has been analyzed. The conditions under which all equilibria exist as well as the stability of every equilibrium point of the system have been investigated. The proposed model conditionally posses two types of bifurcations, Hopf bifurcation, and saddle-node bifurcation. The saddle-node bifurcation has been analyzed, where the bifurcation parameter is harvesting rate. The existence of a maximum sustainable yield to ensure both populations coexist has been discussed. The results give a clear idea that, if the harvesting rate is chosen at a proper value lesser than the maximum sustainable yield then both populations will coexist and the ecological balance will be maintained. The calculation of the first Lyapunov number provides the Hopf bifurcation direction. To verify our analytical results, several numerical simulations have been carried out. Dynamical behaviors of discrete predator-prey model with Holling type IV functional response https://zbmath.org/1485.92098 2022-06-24T15:10:38.853281Z "Rida, S. Z." https://zbmath.org/authors/?q=ai:rida.saad-zagloul "Gouda, Y. Gh." https://zbmath.org/authors/?q=ai:gouda.yasien-ghallab "Zaki, A. S." https://zbmath.org/authors/?q=ai:zaki.a-s This paper is concerned with a discrete-time predator-prey model with Holling type IV functional response. Authors first introduced the local stability analysis of the model and then studied the bifurcation phenomena at the fixed points of the model by using bifurcation theory and the center manifold theorem. Bifurcation types (include flip and Neimark-Sacker) are addressed. Finally, authors gave numerical simulations to check the obtained theoretical results. Reviewer: Wan-Tong Li (Lanzhou) Non-linear population discrete models with two time scales: re-scaling of part of the slow process https://zbmath.org/1485.92099 2022-06-24T15:10:38.853281Z "Sanz, Luis" https://zbmath.org/authors/?q=ai:sanz.luis "Bravo de la Parra, Rafael" https://zbmath.org/authors/?q=ai:bravo-de-la-parra.rafael "Marvá, Marcos" https://zbmath.org/authors/?q=ai:marva.marcos "Sánchez, Eva" https://zbmath.org/authors/?q=ai:sanchez.eva Summary: In this work we present a reduction result for discrete-time systems with two time scales. In order to be valid, previous results in the field require some strong hypotheses that are difficult to check in practical applications. Roughly speaking, the iterates of a map as well as their differentials must converge uniformly on compact sets. Here, we eliminate the hypothesis of uniform convergence of the differentials at no significant cost in the conclusions of the result. This new result is then used to extend to non-linear cases the reduction of some population discrete models involving processes acting at different time scales. In practical cases, some processes that occur at a fast time scale are often only measured at slow time intervals, notably mortality. For a general class of linear models that include such a kind of processes, it has been shown that a more realistic approach requires the re-scaling of those processes to be considered at the fast time scale. We develop the same type of re-scaling in some non-linear models and prove the corresponding reduction results. We also provide an application to a particular model of a structured population in a two-patch environment. Stability, bifurcation, and chaos control of a novel discrete-time model involving Allee effect and cannibalism https://zbmath.org/1485.92100 2022-06-24T15:10:38.853281Z "Shabbir, Muhammad Sajjad" https://zbmath.org/authors/?q=ai:shabbir.muhammad-sajjad "Din, Qamar" https://zbmath.org/authors/?q=ai:din.qamar "Ahmad, Khalil" https://zbmath.org/authors/?q=ai:ahmad.khalil "Tassaddiq, Asifa" https://zbmath.org/authors/?q=ai:tassaddiq.asifa "Soori, Atif Hassan" https://zbmath.org/authors/?q=ai:soori.atif-hassan "Khan, Muhammad Asif" https://zbmath.org/authors/?q=ai:khan.muhammad-asif Summary: This paper is related to some dynamical aspects of a class of predator-prey interactions incorporating cannibalism and Allee effects for non-overlapping generations. Cannibalism has been frequently observed in natural populations, and it has an ability to alter the functional response concerning prey-predator interactions. On the other hand, from dynamical point of view cannibalism is considered as a procedure of stabilization or destabilization within predator-prey models. Taking into account the cannibalism in prey population and with addition of Allee effects, a new discrete-time system is proposed and studied in this paper. Moreover, existence of fixed points and their local dynamics are carried out. It is verified that the proposed model undergoes transcritical bifurcation about its trivial fixed point and period-doubling bifurcation around its boundary fixed point. Furthermore, it is also proved that the proposed system undergoes both period-doubling and Neimark-Sacker bifurcations (NSB) around its interior fixed point. Our study demonstrates that outbreaks of periodic nature may appear due to implementation of cannibalism in prey population, and these periodic oscillations are limited to prey density only without leaving an influence on predation. To restrain this periodic disturbance in prey population density, and other fluctuating and bifurcating behaviors of the model, various chaos control methods are applied. At the end, numerical simulations are presented to illustrate the effectiveness of our theoretical findings. Turing-Hopf bifurcation of a ratio-dependent predator-prey model with diffusion https://zbmath.org/1485.92101 2022-06-24T15:10:38.853281Z "Shi, Qiushuang" https://zbmath.org/authors/?q=ai:shi.qiushuang "Liu, Ming" https://zbmath.org/authors/?q=ai:liu.ming.4|liu.ming.1|liu.ming|liu.ming.3|liu.ming.2 "Xu, Xiaofeng" https://zbmath.org/authors/?q=ai:xu.xiaofeng Summary: In this paper, the Turing-Hopf bifurcation of a ratio-dependent predator-prey model with diffusion and Neumann boundary condition is considered. Firstly, we present a kind of double parameters selection method, which can be used to analyze the Turing-Hopf bifurcation of a general reaction-diffusion equation under Neumann boundary condition. By analyzing the distribution of eigenvalues, the stable region, the unstable region (including Turing unstable region), and Turing-Hopf bifurcation point are derived in a double parameters plane. Secondly, by applying this method, the Turing-Hopf bifurcation of a ratio-dependent predator-prey model with diffusion is investigated. Finally, we compute normal forms near Turing-Hopf singularity and verify the theoretical analysis by numerical simulations. A non-autonomous Leslie-Gower model with Holling type IV functional response and harvesting complexity https://zbmath.org/1485.92102 2022-06-24T15:10:38.853281Z "Song, Jie" https://zbmath.org/authors/?q=ai:song.jie "Xia, Yonghui" https://zbmath.org/authors/?q=ai:xia.yonghui "Bai, Yuzhen" https://zbmath.org/authors/?q=ai:bai.yuzhen "Cai, Yaoxiong" https://zbmath.org/authors/?q=ai:cai.yaoxiong "O'Regan, D." https://zbmath.org/authors/?q=ai:oregan.donal Summary: This paper considers a non-autonomous modified Leslie-Gower model with Holling type IV functional response and nonlinear prey harvesting. The permanence of the model is obtained, and sufficient conditions for the existence of a periodic solution are presented. Two examples and their simulations show the validity of our results. The effect of the defensive strategy taken by the prey on predator-prey interaction https://zbmath.org/1485.92103 2022-06-24T15:10:38.853281Z "Souna, Fethi" https://zbmath.org/authors/?q=ai:souna.fethi "Lakmeche, Abdelkader" https://zbmath.org/authors/?q=ai:lakmeche.abdelkader "Djilali, Salih" https://zbmath.org/authors/?q=ai:djilali.salih A two-predator vs. one-prey predator-model model was proposed, where one predator grows in Malthusian way while the other one in time-delayed logistic manner and with functional response of group-defensive type. To study the impact of the strategy considered by the prey population on the evolution of the studied species, a couple of dynamics such as Hopf bifurcation in both the absence and the presence of time lags are disclosed and the stability of the periodic solution generated by the presence of the time lags are also discussed using the normal form. Some numerical simulations are provided for ensuring the obtained mathematical results. Reviewer: Shengqiang Liu (Harbin) The influence of partial closure for the populations to a non-selective harvesting Lotka-Volterra discrete amensalism model https://zbmath.org/1485.92104 2022-06-24T15:10:38.853281Z "Su, Qianqian" https://zbmath.org/authors/?q=ai:su.qianqian "Chen, Fengde" https://zbmath.org/authors/?q=ai:chen.fengde Summary: In this paper, a non-selective harvesting Lotka-Volterra amensalism discrete model incorporating partial closure for the populations is proposed and studied. By applying the relevant conclusions of difference inequality and some calculation technique, sufficient conditions are obtained to ensure the permanence and extinction of the system. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global attractivity of the system are obtained. Finally, numerical simulations show the feasibility of our results. Stochastic Hopf-Hopf bifurcation of two-species discrete coupling logistic system with symbiotic interaction https://zbmath.org/1485.92105 2022-06-24T15:10:38.853281Z "Yang, Maosong" https://zbmath.org/authors/?q=ai:yang.maosong "Ma, Shaojuan" https://zbmath.org/authors/?q=ai:ma.shaojuan Summary: In this paper, stochastic Hopf-Hopf bifurcation of the discrete coupling logistic system with symbiotic interaction is investigated. Firstly, orthogonal polynomial approximation of discrete random function in the Hilbert spaces is applied to reduce the discrete coupling logistic system with random parameter to the deterministic equivalent system. Then, it is concluded that Hopf-Hopf bifurcation exists in the equivalent deterministic system according to the principle of algebraic criteria. Numerical simulations show that the bifurcation critical value varies with the intensity of random parameter, and Hopf-Hopf bifurcation and period-doubling bifurcation behavior exist. In particular, Hopf-Hopf bifurcation can be drift with the change of random intensity, and frequency locking phenomenon occurs in the stochastic system. Break-even concentration and periodic behavior of a stochastic chemostat model with seasonal fluctuation https://zbmath.org/1485.92106 2022-06-24T15:10:38.853281Z "Zhao, Dianli" https://zbmath.org/authors/?q=ai:zhao.dianli "Yuan, Sanling" https://zbmath.org/authors/?q=ai:yuan.sanling Summary: This paper formulates a single-species stochastic chemostat model with periodic coefficients due to seasonal fluctuation. When the noise is small, a modified break-even concentration is identified, whose value below or above the averaged concentration of the input nutrient can completely determine whether the microorganism will persist or not, where an accuracy decay rate is given for extinction. In case of persistence, existence of the random positive periodic solution is proved for the considered model. Further, the random periodic solution is shown to be globally attractive under some mild extra condition. The periodic dynamics obtained in this paper are supported by computer simulations. Stability and bifurcation analysis of an amensalism system with Allee effect https://zbmath.org/1485.92107 2022-06-24T15:10:38.853281Z "Zhao, Ming" https://zbmath.org/authors/?q=ai:zhao.ming.2|zhao.ming|zhao.ming.1 "Du, Yunfei" https://zbmath.org/authors/?q=ai:du.yunfei Summary: In this work, we propose and study a new amensalism system with Allee effect on the first species. First, we investigate the existence and stability of all possible coexistence equilibrium points and boundary equilibrium points of this system. Then, applying the Sotomayor theorem, we prove that there exists a saddle-node bifurcation under some suitable parameter conditions. Finally, we provide a specific example with corresponding numerical simulations to further demonstrate our theoretical results. Mathematical analysis of tuberculosis control model using nonsingular kernel type Caputo derivative https://zbmath.org/1485.92108 2022-06-24T15:10:38.853281Z "Ahmad, Saeed" https://zbmath.org/authors/?q=ai:ahmad.saeed "Ullah, Rafi" https://zbmath.org/authors/?q=ai:ullah.rafi "Baleanu, Dumitru" https://zbmath.org/authors/?q=ai:baleanu.dumitru-i Summary: This research work investigates some theoretical and semi-analytical results for the mathematical model of tuberculosis disease via derivative due to Caputo and Fabrizio. The concerned derivative involves exponential kernel and very recently it has been adapted for various applied problems. The required results are established by using some fixed point approach of Krasnoselskii and Banach. Further, by the use of iterative tools of Adomian decomposition and Laplace, the semi-analytical results are studied. Some graphical results are given with discussion. Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis https://zbmath.org/1485.92109 2022-06-24T15:10:38.853281Z "Alqahtani, Rubayyi T." https://zbmath.org/authors/?q=ai:alqahtani.rubayyi-turki Summary: In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number $$R_0$$ is less than unity and unstable when $$R_0 > 1$$. The analysis shows that the phenomenon of backward bifurcation occurs when $$R_0<1$$. Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders. Mathematical model of COVID-19 spread in Turkey and south Africa: theory, methods, and applications https://zbmath.org/1485.92110 2022-06-24T15:10:38.853281Z "Atangana, Abdon" https://zbmath.org/authors/?q=ai:atangana.abdon "İğret Araz, Seda" https://zbmath.org/authors/?q=ai:igret-araz.seda Summary: A comprehensive study about the spread of COVID-19 cases in Turkey and South Africa has been presented in this paper. An exhaustive statistical analysis was performed using data collected from Turkey and South Africa within the period of 11 March 2020 to 3 May 2020 and 05 March and 3 of May, respectively. It was observed that in the case of Turkey, a negative Spearman correlation for the number of infected class and a positive Spearman correlation for both the number of deaths and recoveries were obtained. This implied that the daily infections could decrease, while the daily deaths and number of recovered people could increase under current conditions. In the case of South Africa, a negative Spearman correlation for both daily deaths and daily infected people were obtained, indicating that these numbers may decrease if the current conditions are maintained. The utilization of a statistical technique predicted the daily number of infected, recovered, and dead people for each country; and three results were obtained for Turkey, namely an upper boundary, a prediction from current situation and lower boundary. The histograms of the daily number of newly infected, recovered and death showed a sign of lognormal and normal distribution, which is presented using the Bell curving method parameters estimation. A new mathematical model COVID-19 comprised of nine classes was suggested; of which a formula of the reproductive number, well-poseness of the solutions and the stability analysis were presented in detail. The suggested model was further extended to the scope of nonlocal operators for each case; whereby a numerical method was used to provide numerical solutions, and simulations were performed for different non-integer numbers. Additionally, sections devoted to control optimal and others dedicated to compare cases between Turkey and South Africa with the aim to comprehend why there are less numbers of deaths and infected people in South Africa than Turkey were presented in detail. Hamiltonian structure of compartmental epidemiological models https://zbmath.org/1485.92111 2022-06-24T15:10:38.853281Z "Ballesteros, Angel" https://zbmath.org/authors/?q=ai:ballesteros.angel "Blasco, Alfonso" https://zbmath.org/authors/?q=ai:blasco.alfonso "Gutierrez-Sagredo, Ivan" https://zbmath.org/authors/?q=ai:gutierrez-sagredo.ivan Summary: Any epidemiological compartmental model with constant population is shown to be a Hamiltonian dynamical system in which the total population plays the role of the Hamiltonian function. Moreover, some particular cases within this large class of models are shown to be bi-Hamiltonian. New interacting compartmental models among different populations, which are endowed with a Hamiltonian structure, are introduced. The Poisson structures underlying the Hamiltonian description of all these dynamical systems are explicitly presented, and their associated Casimir functions are shown to provide an efficient tool in order to find exact analytical solutions for epidemiological models, such as the ones describing the dynamics of the COVID-19 pandemic. Accurate closed-form solution of the SIR epidemic model https://zbmath.org/1485.92112 2022-06-24T15:10:38.853281Z "Barlow, Nathaniel S." https://zbmath.org/authors/?q=ai:barlow.nathaniel-s "Weinstein, Steven J." https://zbmath.org/authors/?q=ai:weinstein.steven-j Summary: An accurate closed-form solution is obtained to the SIR epidemic model through the use of asymptotic approximants [the authors et al., Q. J. Mech. Appl. Math. 70, No. 1, 21--48 (2017; Zbl 1435.41030)]. The solution is created by analytically continuing the divergent power series solution such that it matches the long-time asymptotic behavior of the epidemic model. The utility of the analytical form is demonstrated through its application to the COVID-19 pandemic. Comparison of fractional order techniques for measles dynamics https://zbmath.org/1485.92113 2022-06-24T15:10:38.853281Z "Bashir, Amna" https://zbmath.org/authors/?q=ai:bashir.amna "Mushtaq, Muhammad" https://zbmath.org/authors/?q=ai:mushtaq.muhammad-umer "Zafar, Zain Ul Abadin" https://zbmath.org/authors/?q=ai:zafar.zain-ul-abadin "Rehan, Kashif" https://zbmath.org/authors/?q=ai:rehan.kashif "Muntazir, Rana Muhammad Akram" https://zbmath.org/authors/?q=ai:muntazir.rana-muhammad-akram Summary: A mathematical model which is non-linear in nature with non-integer order $$\varphi, 0 < \phi \leq 1$$ is presented for exploring the SIRV model with the rate of vaccination $$\mu_1$$ and rate of treatment $$\mu_2$$ to describe a measles model. Both the disease free $$\mathcal{F}_0$$ and the endemic $$\mathcal{F}^\ast$$ points have been calculated. The stability has also been argued for using the theorem of stability of non-integer order differential equations. $$\mathcal{R}_0$$, the basic reproduction number exhibits an imperative role in the stability of the model. The disease free equilibrium point $$\mathcal{F}_0$$ is an attractor when $$\mathcal{R}_0 < 1$$. For $$\mathcal{R}_0 > 1, \mathcal{F}_0$$ is unstable, the endemic equilibrium $$\mathcal{F}^\ast$$ subsists and it is an attractor. Numerical simulations of considerable model are also supported to study the behavior of the system. Bayesian inference for a susceptible-exposed-infected-recovered epidemic model with data augmentation https://zbmath.org/1485.92114 2022-06-24T15:10:38.853281Z "Beldjoudi, Chouaib" https://zbmath.org/authors/?q=ai:beldjoudi.chouaib "Kernane, Tewfik" https://zbmath.org/authors/?q=ai:kernane.tewfik "El Maroufy, Hamid" https://zbmath.org/authors/?q=ai:el-maroufy.hamid Summary: A Bayesian data-augmentation method allows estimating the parameters in a susceptible-exposed-infected-recovered (SEIR) epidemic model, which is formulated as a continuous-time Markov process and approximated by a diffusion process using the convergence of the master equation. The estimation was carried out with latent data points between every pair of observations simulated through the Euler-Maruyama scheme, which involves imputing the missing data in addition to the model parameters. The missing data and parameters are treated as random variables, and a Markov chain Monte Carlo algorithm updates the missing data and the parameter values. Numerical simulations show the effectiveness of the proposed Markov-chain Monte Carlo algorithm. The challenges of modeling and forecasting the spread of COVID-19 https://zbmath.org/1485.92115 2022-06-24T15:10:38.853281Z "Bertozzi, Andrea L." https://zbmath.org/authors/?q=ai:bertozzi.andrea-louise "Franco, Elisa" https://zbmath.org/authors/?q=ai:franco.elisa "Sledge, Daniel" https://zbmath.org/authors/?q=ai:sledge.daniel Summary: The coronavirus disease 2019 (COVID-19) pandemic has placed epidemic modeling at the forefront of worldwide public policy making. Nonetheless, modeling and forecasting the spread of COVID-19 remains a challenge. Here, we detail three regional-scale models for forecasting and assessing the course of the pandemic. This work demonstrates the utility of parsimonious models for early-time data and provides an accessible framework for generating policy-relevant insights into its course. We show how these models can be connected to each other and to time series data for a particular region. Capable of measuring and forecasting the impacts of social distancing, these models highlight the dangers of relaxing nonpharmaceutical public health interventions in the absence of a vaccine or antiviral therapies. An analysis of tuberculosis model with exponential decay law operator https://zbmath.org/1485.92116 2022-06-24T15:10:38.853281Z "Bonyah, Ebenezer" https://zbmath.org/authors/?q=ai:bonyah.ebenezer "Fatmawati" https://zbmath.org/authors/?q=ai:fatmawati. Summary: In this paper, we explore the dynamics of tuberculosis (TB) epidemic model that includes the recruitment rate in both susceptible and infected population. Stability and sensitivity analysis of the classical TB model is carried out. Caputo-Fabrizio (CF) operator is then used to explain the dynamics of the TB model. The concept of fixed point theory is employed to obtain the existence and uniqueness of the solution of the TB model in the light of CF operator. Numerical simulations based on homotopy analysis transform method (HATM) and Padé approximations are performed to obtain qualitative information on the model. Numerical solutions depict that the order of the fractional derivative has great dynamics of the TB model. Modeling fractional-order dynamics of syphilis via Mittag-Leffler law https://zbmath.org/1485.92117 2022-06-24T15:10:38.853281Z "Bonyah, E." https://zbmath.org/authors/?q=ai:bonyah.ebenezer "Chukwu, C. W." https://zbmath.org/authors/?q=ai:chukwu.c-w "Juga, M. L." https://zbmath.org/authors/?q=ai:juga.m-l "Fatmawati" https://zbmath.org/authors/?q=ai:fatmawati. Summary: Syphilis is one the most dangerous sexually transmitted disease which is common in the world. In this work, we formulate and analyze a mathematical model of Syphilis with an emphasis on treatment in the sense of Caputo-Fabrizio (CF) and Atangana-Baleanu (Mittag-Leffler law) derivatives. The basic reproduction number of the CF model which presents information on the spread of the disease is determined. The model's steady states were found, and the disease-free state's local and global stability are established based on the basic reproduction number. The existence and uniqueness of solutions for both Caputo-Fabrizio and Atangana-Baleanu derivative in the Caputo sense are established. Numerical simulations were carried out to support the analytical solution, which indicates that the fractional-order derivatives influence the dynamics of the spread of Syphilis in any community induced with the disease. The turning point and end of an expanding epidemic cannot be precisely forecast https://zbmath.org/1485.92118 2022-06-24T15:10:38.853281Z "Castro, Mario" https://zbmath.org/authors/?q=ai:castro.mario-h "Ares, Saúl" https://zbmath.org/authors/?q=ai:ares.saul "Manrubia, Susanna" https://zbmath.org/authors/?q=ai:manrubia.susanna-c Summary: Epidemic spread is characterized by exponentially growing dynamics, which are intrinsically unpredictable. The time at which the growth in the number of infected individuals halts and starts decreasing cannot be calculated with certainty before the turning point is actually attained; neither can the end of the epidemic after the turning point. A susceptible--infected--removed (SIR) model with confinement (SCIR) illustrates how lockdown measures inhibit infection spread only above a threshold that we calculate. The existence of that threshold has major effects in predictability: A Bayesian fit to the COVID-19 pandemic in Spain shows that a slowdown in the number of newly infected individuals during the expansion phase allows one to infer neither the precise position of the maximum nor whether the measures taken will bring the propagation to the inhibition regime. There is a short horizon for reliable prediction, followed by a dispersion of the possible trajectories that grows extremely fast. The impossibility to predict in the midterm is not due to wrong or incomplete data, since it persists in error-free, synthetically produced datasets and does not necessarily improve by using larger datasets. Our study warns against precise forecasts of the evolution of epidemics based on mean-field, effective, or phenomenological models and supports that only probabilities of different outcomes can be confidently given. Using observed incidence to calibrate the transmission level of a mathematical model for \textit{Plasmodium vivax} dynamics including case management and importation https://zbmath.org/1485.92119 2022-06-24T15:10:38.853281Z "Champagne, Clara" https://zbmath.org/authors/?q=ai:champagne.clara "Gerhards, Maximilian" https://zbmath.org/authors/?q=ai:gerhards.maximilian "Lana, Justin" https://zbmath.org/authors/?q=ai:lana.justin "García Espinosa, Bernardo" https://zbmath.org/authors/?q=ai:garcia-espinosa.bernardo "Bradley, Christina" https://zbmath.org/authors/?q=ai:bradley.christina "González, Oscar" https://zbmath.org/authors/?q=ai:gonzalez.oscar-e|gonzalez.oscar-r "Cohen, Justin M." https://zbmath.org/authors/?q=ai:cohen.justin-m "Le Menach, Arnaud" https://zbmath.org/authors/?q=ai:le-menach.arnaud "White, Michael T." https://zbmath.org/authors/?q=ai:white.michael-t "Pothin, Emilie" https://zbmath.org/authors/?q=ai:pothin.emilie Summary: In this work, we present a simple and flexible model for \textit{Plasmodium vivax} dynamics which can be easily combined with routinely collected data on local and imported case counts to quantify transmission intensity and simulate control strategies. This model extends the model from [\textit{M. T. White} et al., Variation in relapse frequency and the transmission potential of \textit{Plasmodium vivax} malaria'', Proc. R. Soc. B, Biol Sci. 283, No. 1827, Article ID 20160048, 9 p. (2016; \url{doi:10.1098/rspb.2016.0048 })] by including case management interventions targeting liver-stage or blood-stage parasites, as well as imported infections. The endemic steady state of the model is used to derive a relationship between the observed incidence and the transmission rate in order to calculate reproduction numbers and simulate intervention scenarios. To illustrate its potential applications, the model is used to calculate local reproduction numbers in Panama and identify areas of sustained malaria transmission that should be targeted by control interventions. Asymptotic behavior and threshold of a stochastic SIQS epidemic model with vertical transmission and Beddington-DeAngelis incidence https://zbmath.org/1485.92120 2022-06-24T15:10:38.853281Z "Chen, Yang" https://zbmath.org/authors/?q=ai:chen.yang.1|chen.yang.2 "Zhao, Wencai" https://zbmath.org/authors/?q=ai:zhao.wencai Summary: This paper investigates a deterministic and stochastic SIQS epidemic model with vertical transmission and Beddington-DeAngelis incidence. Firstly, for the corresponding deterministic system, the global asymptotic stability of disease-free equilibrium and the endemic equilibrium is proved through the stability theory. Secondly, for the stochastic system, the threshold conditions which decide the extinction or permanence of the disease are derived. By constructing suitable Lyapunov functions, we investigate the oscillation behavior of the stochastic system solution near the endemic equilibrium. The results of this paper show that there exists a great difference between the deterministic and stochastic systems, which implies that the large stochastic noise contributes to inhibiting the spread of disease. Finally, in order to validate the theoretical results, a series of numerical simulations are presented. Optimal control of the SIR model with constrained policy, with an application to COVID-19 https://zbmath.org/1485.92121 2022-06-24T15:10:38.853281Z "Ding, Yujia" https://zbmath.org/authors/?q=ai:ding.yujia "Schellhorn, Henry" https://zbmath.org/authors/?q=ai:schellhorn.henry Summary: This article considers the optimal control of the SIR model with both transmission and treatment uncertainty. It follows the model presented in [\textit{N. M. Gatto} and the second author, Math. Biosci. 333, Article ID 108539, 11 p. (2021; Zbl 1474.92102)]. We make four significant improvements on the latter paper. First, we prove the existence of a solution to the model. Second, our interpretation of the control is more realistic: while in [loc. cit.] the control $$\alpha$$ is the proportion of the population that takes a basic dose of treatment, so that $$\alpha > 1$$ occurs only if some patients take more than a basic dose, in our paper, $$\alpha$$ is constrained between zero and one, and represents thus the \textit{proportion of the population} undergoing treatment. Third, we provide a complete solution for the moderate infection regime (with constant treatment). Finally, we give a thorough interpretation of the control in the moderate infection regime, while [loc. cit.] focused on the interpretation of the low infection regime. Finally, we compare the efficiency of our control to curb the COVID-19 epidemic to other types of control. A two diffusion stochastic model for the spread of the new corona virus SARS-CoV-2 https://zbmath.org/1485.92122 2022-06-24T15:10:38.853281Z "Đorđević, J." https://zbmath.org/authors/?q=ai:dordevic.jovanka|dordevic.jasmina "Papić, I." https://zbmath.org/authors/?q=ai:papic.ivan "Šuvak, N." https://zbmath.org/authors/?q=ai:suvak.nenad Summary: We propose a refined version of the stochastic SEIR model for epidemic of the new corona virus SARS-Cov-2, causing the COVID-19 disease, taking into account the spread of the virus due to the regular infected individuals (transmission coefficient $$\beta$$), hospitalized individuals (transmission coefficient $$l\beta$$, $$l>0$$) and superspreaders (transmission coefficient $$\beta'$$). The model is constructed from the corresponding ordinary differential model by introducing two independent environmental white noises in transmission coefficients for above mentioned classes -- one noise for infected and hospitalized individuals and the other for superspreaders. Therefore, the model is defined as a system of stochastic differential equations driven by two independent standard Brownian motions. Existence and uniqueness of the global positive solution is proven, and conditions under which extinction and persistence in mean hold are given. The theoretical results are illustrated via numerical simulations. \textit{Shigellosis} dynamics: modelling the effects of treatment, sanitation, and education in the presence of carriers https://zbmath.org/1485.92123 2022-06-24T15:10:38.853281Z "Edward, Stephen" https://zbmath.org/authors/?q=ai:edward.stephen "Mureithi, Eunice" https://zbmath.org/authors/?q=ai:mureithi.eunice-w "Shaban, Nyimvua" https://zbmath.org/authors/?q=ai:shaban.nyimvua This paper focus on a Shigellosis model including disease carriers with multiple control strategies is developed. The effective reproductive number $$R_e$$ was obtained. Based on this threshold, the dynamics for the model was studied. More specifically, the disease-free equilibrium for the model is locally asymptotically stable if $$R_e < 1$$ and unstable if $$R_e > 1$$. Further, by using Lyapunov functions, the disease-free equilibrium for the model was shown to be globally asymptotically stable if $$R_e < 1$$ and unstable if $$R_e > 1$$, while the endemic equilibrium for the model is globally asymptotically stable if $$R_e > 1$$. Sensitivity analysis was performed to investigate the parameters that have a high impact on the transmission dynamics of the disease with direct transmission contributing more infections than indirect transmission. Numerical results shown that there is a reduction in the number of infections when at least a single control measure is applied efficiently. Results also shown that carriers play a potential role in the prevalence of Shigellosis and ignoring these individuals could potentially undermine the efforts of containing this epidemic. Reviewer: Ran Zhang (Nanjing) Stability of discrete-time HIV dynamics models with three categories of infected CD $$4^+$$ T-cells https://zbmath.org/1485.92124 2022-06-24T15:10:38.853281Z "Elaiw, A. M." https://zbmath.org/authors/?q=ai:elaiw.ahmed-m "Alshaikh, M. A." https://zbmath.org/authors/?q=ai:alshaikh.matuka-a Summary: This paper studies the global stability of two discrete-time HIV infection models. The models integrate (i) latently infected cells, (ii) long-lived chronically infected cells and (iii) short-lived infected cells. The second model generalizes the first one by assuming that the incidence rate of infection as well as the production and removal rates of the HIV particles and cells are modeled by general nonlinear functions. We discretize the continuous-time models by using a nonstandard finite difference scheme. The positivity and boundedness of solutions are established. The basic reproduction number is derived. By using the Lyapunov method, we prove the global stability of the models. Numerical simulations are presented to illustrate our theoretical results. Bayesian forecast of the basic reproduction number during the COVID-19 epidemic in Morocco and Italy https://zbmath.org/1485.92125 2022-06-24T15:10:38.853281Z "El Fatini, Mohamed" https://zbmath.org/authors/?q=ai:el-fatini.mohamed "El Khalifi, Mohamed" https://zbmath.org/authors/?q=ai:el-khalifi.mohamed "Gerlach, Richard" https://zbmath.org/authors/?q=ai:gerlach.richard-h "Pettersson, Roger" https://zbmath.org/authors/?q=ai:pettersson.roger Summary: In a COVID-19 susceptible-infected-recovered-dead model with time-varying rates of transmission, recovery, and death, the parameters are constant in small time intervals. A posteriori parameters result from the Euler-Maruyama approximation for stochastic differential equations and from Bayes' theorem. Parameter estimates and 10-day predictions are performed based on Moroccan and Italian COVID-19 data. Mean absolute errors and mean square errors indicate that predictions are of good quality. A fractional complex network model for novel corona virus in China https://zbmath.org/1485.92126 2022-06-24T15:10:38.853281Z "El-Saka, H. A. A." https://zbmath.org/authors/?q=ai:el-saka.hala-a-a "Obaya, I." https://zbmath.org/authors/?q=ai:obaya.i "Agiza, H. N." https://zbmath.org/authors/?q=ai:agiza.hamdy-n Summary: As is well known the novel coronavirus (COVID-19) is a zoonotic virus and our model is concerned with the effect of the zoonotic source of the coronavirus during the outbreak in China. We present a SEIS complex network epidemic model for the novel coronavirus. Our model is presented in fractional form and with varying population. The steady states and the basic reproductive number are calculated. We also present some numerical examples and the sensitivity analysis of the basic reproductive number for the parameters. System response of an alcoholism model under the effect of immigration via non-singular kernel derivative https://zbmath.org/1485.92127 2022-06-24T15:10:38.853281Z "Evirgen, Fırat" https://zbmath.org/authors/?q=ai:evirgen.firat "Uçar, Sümeyra" https://zbmath.org/authors/?q=ai:ucar.sumeyra "Özdemir, Necati" https://zbmath.org/authors/?q=ai:ozdemir.necati "Hammouch, Zakia" https://zbmath.org/authors/?q=ai:hammouch.zakia Summary: In this study, we aim to comprehensively investigate a drinking model connected to immigration in terms of Atangana-Baleanu derivative in Caputo type. To do this, we firstly extend the model describing drinking model by changing the derivative with time fractional derivative having Mittag-Leffler kernel. The existence and uniqueness of the drinking model solutions together with the stability analysis is shown by the help of Banach fixed point theorem. The special solution of the model is investigated using the Sumudu transformation and then, we present some numerical simulations for the different fractional orders to emphasize the effectiveness of the used derivative. Epidemiological analysis of fractional order COVID-19 model with Mittag-Leffler kernel https://zbmath.org/1485.92128 2022-06-24T15:10:38.853281Z "Farman, Muhammad" https://zbmath.org/authors/?q=ai:farman.muhammad "Akgül, Ali" https://zbmath.org/authors/?q=ai:akgul.ali "Nisar, Kottakkaran Sooppy" https://zbmath.org/authors/?q=ai:sooppy-nisar.kottakkaran "Ahmad, Dilshad" https://zbmath.org/authors/?q=ai:ahmad.dilshad "Ahmad, Aqeel" https://zbmath.org/authors/?q=ai:ahmad.aqeel.1 "Kamangar, Sarfaraz" https://zbmath.org/authors/?q=ai:kamangar.sarfaraz "Saleel, C. Ahamed" https://zbmath.org/authors/?q=ai:saleel.c-ahamed Summary: This paper derived fractional derivatives with Atangana-Baleanu, Atangana-Toufik scheme and fractal fractional Atangana-Baleanu sense for the COVID-19 model. These are advanced techniques that provide effective results to analyze the COVID-19 outbreak. Fixed point theory is used to derive the existence and uniqueness of the fractional-order model COVID-19 model. We also proved the property of boundedness and positivity for the fractional-order model. The Atangana-Baleanu technique and Fractal fractional operator are used with the Sumudu transform to find reliable results for fractional order COVID-19 Model. The generalized Mittag-Leffler law is also used to construct the solution with the different fractional operators. Numerical simulations are performed for the developed scheme in the range of fractional order values to explain the effects of COVID-19 at different fractional values and justify the theoretical outcomes, which will be helpful to understand the outbreak of COVID-19 and for control strategies. New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019-nCoV system https://zbmath.org/1485.92129 2022-06-24T15:10:38.853281Z "Gao, Wei" https://zbmath.org/authors/?q=ai:gao.wei.3 "Baskonus, Haci Mehmet" https://zbmath.org/authors/?q=ai:baskonus.haci-mehmet "Shi, Li" https://zbmath.org/authors/?q=ai:shi.li Summary: According to the report presented by the World Health Organization, a new member of viruses, namely, coronavirus, shortly 2019-nCoV, which arised in Wuhan, China, on January 7, 2020, has been introduced to the literature. The main aim of this paper is investigating and finding the optimal values for better understanding the mathematical model of the transfer of 2019-nCoV from the reservoir to people. This model, named Bats-Hosts-Reservoir-People coronavirus (BHRPC) model, is based on bats as essential animal beings. By using a powerful numerical method we obtain simulations of its spreading under suitably chosen parameters. Whereas the obtained results show the effectiveness of the theoretical method considered for the governing system, the results also present much light on the dynamic behavior of the Bats-Hosts-Reservoir-People transmission network coronavirus model. Analysis of cholera epidemic controlling using mathematical modeling https://zbmath.org/1485.92130 2022-06-24T15:10:38.853281Z "Hailemariam Hntsa, Kinfe" https://zbmath.org/authors/?q=ai:hailemariam-hntsa.kinfe "Nerea Kahsay, Berhe" https://zbmath.org/authors/?q=ai:nerea-kahsay.berhe In this paper, a mathematical model for the transmission dynamics of cholera was studied. The basic reproductive number $$R_0$$ was obtained. Based on this threshold, the dynamics for the model was studied. More specifically, the cholera-free equilibrium for the model is locally asymptotically stable if $$R_0 < 1$$ and unstable if $$R_0> 1$$. Further, by using Lyapunov functions, the cholera-free equilibrium for the model was shown to be globally asymptotically stable if $$R_0 < 1$$ and unstable if $$R_0 > 1$$, while the endemic equilibrium for the model is globally asymptotically stable if $$R_0> 1$$. For $$R_0=1$$, the forward bifurcation was shown. Numerical simulations are carried out to validate the theoretical results, which indicates that the disease dies out in areas with adequate preventive measures and widespread and kills more people in areas with the inadequate preventive measures. Reviewer: Ran Zhang (Nanjing) Strong spatial embedding of social networks generates nonstandard epidemic dynamics independent of degree distribution and clustering https://zbmath.org/1485.92131 2022-06-24T15:10:38.853281Z "Haw, David J." https://zbmath.org/authors/?q=ai:haw.david-j "Pung, Rachael" https://zbmath.org/authors/?q=ai:pung.rachael "Riley, Steven" https://zbmath.org/authors/?q=ai:riley.steven Summary: Some directly transmitted human pathogens, such as influenza and measles, generate sustained exponential growth in incidence and have a high peak incidence consistent with the rapid depletion of susceptible individuals. Many do not. While a prolonged exponential phase typically arises in traditional disease-dynamic models, current quantitative descriptions of nonstandard epidemic profiles are either abstract, phenomenological, or rely on highly skewed offspring distributions in network models. Here, we create large socio-spatial networks to represent contact behavior using human population-density data, a previously developed fitting algorithm, and gravity-like mobility kernels. We define a basic reproductive number $$R_0$$ for this system, analogous to that used for compartmental models. Controlling for $$R_0$$, we then explore networks with a household--workplace structure in which between-household contacts can be formed with varying degrees of spatial correlation, determined by a single parameter from the gravity-like kernel. By varying this single parameter and simulating epidemic spread, we are able to identify how more frequent local movement can lead to strong spatial correlation and, thus, induce subexponential outbreak dynamics with lower, later epidemic peaks. Also, the ratio of peak height to final size was much smaller when movement was highly spatially correlated. We investigate the topological properties of our networks via a generalized clustering coefficient that extends beyond immediate neighborhoods, identifying very strong correlations between fourth-order clustering and nonstandard epidemic dynamics. Our results motivate the observation of both incidence and socio-spatial human behavior during epidemics that exhibit nonstandard incidence patterns. Existence of solution and stability for the fractional order novel coronavirus (nCoV-2019) model https://zbmath.org/1485.92132 2022-06-24T15:10:38.853281Z "Hussain, Azhar" https://zbmath.org/authors/?q=ai:hussain.azhar "Baleanu, Dumitru" https://zbmath.org/authors/?q=ai:baleanu.dumitru-i "Adeel, Muhammad" https://zbmath.org/authors/?q=ai:adeel.muhammad Summary: The aim of this work is to present a new fractional order model of novel coronavirus (nCoV-2019) under Caputo-Fabrizio derivative. We make use of fixed point theory and Picard-Lindelöf technique to explore the existence and uniqueness of solution for the proposed model. Moreover, we explore the generalized Hyers-Ulam stability of the model using Gronwall's inequality. Dynamical system of the growth of COVID-19 with controller https://zbmath.org/1485.92133 2022-06-24T15:10:38.853281Z "Ibrahim, Rabha W." https://zbmath.org/authors/?q=ai:ibrahim.rabha-waell "Altulea, Dania" https://zbmath.org/authors/?q=ai:altulea.dania "Elobaid, Rafida M." https://zbmath.org/authors/?q=ai:elobaid.rafida-m Summary: Recently, various studied were presented to describe the population dynamic of COVID-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel. Bifurcation analysis of a \textit{chikungunya} transmission model https://zbmath.org/1485.92134 2022-06-24T15:10:38.853281Z "Kambiré, Famane" https://zbmath.org/authors/?q=ai:kambire.famane "Somé, Blaise" https://zbmath.org/authors/?q=ai:some.blaise (no abstract) A fractional order COVID-19 epidemic model with Mittag-Leffler kernel https://zbmath.org/1485.92135 2022-06-24T15:10:38.853281Z "Khan, Hasib" https://zbmath.org/authors/?q=ai:khan.hasib "Ibrahim, Muhammad" https://zbmath.org/authors/?q=ai:ibrahim.muhammad-jamilu|ibrahim.muhammad-talal "Abdel-Aty, Abdel-Haleem" https://zbmath.org/authors/?q=ai:abdel-aty.abdel-haleem "Khashan, M. Motawi" https://zbmath.org/authors/?q=ai:khashan.m-motawi "Khan, Farhat Ali" https://zbmath.org/authors/?q=ai:khan.farhat-ali "Khan, Aziz" https://zbmath.org/authors/?q=ai:khan.aziz Summary: In this article, we are studying fractional-order COVID-19 model for the analytical and computational aspects. The model consists of five compartments including; $$S_c$$'' which denotes susceptible class, $$E_c$$'' represents exposed population, $$I_c$$'' is the class for infected people who have been developed with COVID-19 and can cause spread in the population. The recovered class is denoted by $$R_c$$'' and $$V_c$$'' is the concentration of COVID-19 virus in the area. The computational study shows us that the spread will be continued for long time and the recovery reduces the infection rate. The numerical scheme is based on the Lagrange's interpolation polynomial and the numerical results for the suggested model are similar to the integer order which gives us the applicability of the numerical scheme and effectiveness of the fractional order derivative. A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying https://zbmath.org/1485.92136 2022-06-24T15:10:38.853281Z "Kumar, Devendra" https://zbmath.org/authors/?q=ai:kumar.devendra.3 "Singh, Jagdev" https://zbmath.org/authors/?q=ai:singh.jagdev "Al Qurashi, Maysaa" https://zbmath.org/authors/?q=ai:al-qurashi.maysaa-mohamed|alqurashi.maysaa-m "Baleanu, Dumitru" https://zbmath.org/authors/?q=ai:baleanu.dumitru-i Summary: The present paper deals with a new fractional SIRS-SI model describing the transmission of malaria disease. The SIRS-SI malaria model is modified by using the Caputo-Fabrizio fractional operator for the inclusion of memory. We also suggest the utilization of vaccines, antimalarial medicines, and spraying for the treatment and control of the malaria disease. The theory of fixed point is utilized to examine the existence of the solution of a fractional SIRS-SI model describing spreading of malaria. The uniqueness of the solution of SIRS-SI model for malaria is also analyzed. It is shown that the treatments have great impact on the dynamical system of human and mosquito populations. The numerical simulation of fractional SIRS-SI malaria model is performed with the aid of HATM and Maple packages to show the effect of different parameters of the treatment of malaria disease. The numerical results for fractional SIRS-SI malaria model reveal that the recommended approach is very accurate and effective. Infection curves on small-world networks are linear only in the vicinity of the critical point https://zbmath.org/1485.92137 2022-06-24T15:10:38.853281Z "Kuśmierz, Łukasz" https://zbmath.org/authors/?q=ai:kusmierz.lukasz "Toyoizumi, Taro" https://zbmath.org/authors/?q=ai:toyoizumi.taro (no abstract) Dynamics of epidemic diseases without guaranteed immunity https://zbmath.org/1485.92138 2022-06-24T15:10:38.853281Z "Langfeld, Kurt" https://zbmath.org/authors/?q=ai:langfeld.kurt Summary: The pandemic of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) suggests a novel type of disease spread dynamics. We here study the case where infected agents recover and only develop immunity if they are continuously infected for some time $$\tau$$. For large $$\tau$$, the disease model is described by a statistical field theory. Hence, the phases of the underlying field theory characterise the disease dynamics: (i) a pandemic phase and (ii) a response regime. The statistical field theory provides an upper bound of the peak rate of infected agents. An effective control strategy needs to aim to keep the disease in the response regime (no second' wave). The model is tested at the quantitative level using an idealised disease network. The model excellently describes the epidemic spread of the SARS-CoV-2 outbreak in the city of Wuhan, China. We find that only 30\% of the recovered agents have developed immunity. Herd immunity levels and multi-strain influenza epidemics in Russia: a modelling study https://zbmath.org/1485.92139 2022-06-24T15:10:38.853281Z "Leonenko, Vasiliy N." https://zbmath.org/authors/?q=ai:leonenko.vasiliy-n Summary: In the present paper, we consider a compartmental epidemic model which simulates the co-circulation of three influenza strains, A(H1N1)pdm09, A(H3N2), and B, in a population with the history of exposure to these virus strains. A strain-specific incidence data for the model input was generated using long-term weekly ARI incidence and virologic testing data. The algorithm for model calibration was developed as a combination of simulated annealing and BFGS optimization methods. Two simulations were carried out, assuming the absence and the presence of protected individuals in the population, with 2017--2018 and 2018--2019 epidemic seasons in Moscow as a case study. It was shown that strain-specific immune levels defined by virologic studies might be used in the model to obtain plausible incidence curves. However, different output parameter values, such as fractions of individuals exposed to particular virus strain in the previous epidemic season, can correspond to similar incidence trajectories, which complicates the assessment of herd immunity levels based on the model calibration. The results of the study will be used in the research of the interplay between the immunity formation dynamics and the circulation of influenza strains in Russian cities. Stability analysis of a fractional-order SIS model on complex networks with linear treatment function https://zbmath.org/1485.92140 2022-06-24T15:10:38.853281Z "Liu, Na" https://zbmath.org/authors/?q=ai:liu.na "Fang, Jie" https://zbmath.org/authors/?q=ai:fang.jie.1 "Deng, Wei" https://zbmath.org/authors/?q=ai:deng.wei "Sun, Jun-wei" https://zbmath.org/authors/?q=ai:sun.junwei Summary: In recent years, many research works have been focusing on the propagation dynamics of infectious diseases in complex networks, and some interesting results have been obtained. The main purpose of this paper is to investigate the stability of a fractional SIS model on complex networks with linear treatment function. Based on the basic reproduction number, the stability of the disease-free equilibrium point and the endemic equilibrium point is analyzed in detail. That is, when $$R_0\leq1$$, the disease-free equilibrium point is globally asymptotically stable and the disease will die out ultimately; when $$R_0>1$$, there exists a unique endemic equilibrium point, and both the disease-free equilibrium point and the endemic equilibrium point are stable and the disease will not spread to all individuals. Finally, numerical simulations are presented to demonstrate the theoretical results. Moreover, the influence of the fractional-order parameter and the coefficient of the linear treatment function on the decay rate of the infectious is depicted separately. Epidemic models with discrete state structures https://zbmath.org/1485.92141 2022-06-24T15:10:38.853281Z "Liu, Suli" https://zbmath.org/authors/?q=ai:liu.suli "Li, Michael Y." https://zbmath.org/authors/?q=ai:li.michael-yi Summary: The state of an infectious disease can represent the degree of infectivity of infected individuals, or susceptibility of susceptible individuals, or immunity of recovered individuals, or a combination of these measures. When the disease progression is long such as for HIV, individuals often experience switches among different states. We derive an epidemic model in which infected individuals have a discrete set of states of infectivity and can switch among different states. The model also incorporates a general incidence form in which new infections are distributed among different disease states. We discuss the importance of the transmission-transfer network for infectious diseases. Under the assumption that the transmission-transfer network is strongly connected, we establish that the basic reproduction number $$\mathcal{R}_0$$ is a sharp threshold parameter: if $$\mathcal{R}_0 \leq 1$$, the disease-free equilibrium is globally asymptotically stable and the disease always dies out; if $$\mathcal{R}_0 > 1$$, the disease-free equilibrium is unstable, the system is uniformly persistent and initial outbreaks lead to persistent disease infection. For a restricted class of incidence functions, we prove that there is a unique endemic equilibrium and it is globally asymptotically stable when $$\mathcal{R}_0 > 1$$. Furthermore, we discuss the impact of different state structures on $$\mathcal{R}_0$$, on the distribution of the disease states at the unique endemic equilibrium, and on disease control and preventions. Implications to the COVID-19 pandemic are also discussed. Fractional study of Huanglongbing model with singular and non-singular kernel https://zbmath.org/1485.92142 2022-06-24T15:10:38.853281Z "Li, Yi Xia" https://zbmath.org/authors/?q=ai:li.yixia "Alshehri, Maryam G." https://zbmath.org/authors/?q=ai:alshehri.maryam-gharamah-ali "Algehyne, Ebrahem A." https://zbmath.org/authors/?q=ai:algehyne.ebrahem-a "Ali, Aatif" https://zbmath.org/authors/?q=ai:ali.aatif "Khan, Muhammad Altaf" https://zbmath.org/authors/?q=ai:khan.muhammad-altaf "Muhammad, Taseer" https://zbmath.org/authors/?q=ai:muhammad.taseer "Islam, Saeed" https://zbmath.org/authors/?q=ai:islam.saeed Summary: The disease of citrus is Huanglongbing (HLB), a Chinese name meaning yellow shoot disease and in English-speaking countries referred as a citrus greening threatening the citrus industries worldwide. Citrus greening associated with Candidatus Liberibacter asiaticus' (CLas), is the most devastating disease spread through the infected citrus trees and the major insect vector, the infected citrus psyllid (Diaphorina citri). A fractional-order compartmental model in Caputo and Atangana-Baleanu sense is consider to study the dynamical aspects of HLB among citrus trees and Asian citrus psyllid (ACP). We computed a basic reproduction number and present a detailed theoretical analysis including solution positivity and the stability of disease-free equilibrium of the Caputo fractional model. Numerical simulations are conducted for both Caputo and Atangana-Baleanu operators. The numerical results of Caputo model suggest that the infection and removal rate impacts impressively on the severity of the HLB. Moreover, for different values of the fractional derivative suggest the infection minimization and possibly the control for the disease. While simulating the model using both the operators, the results captured are are better and may be useful in further research of the proposed model. We conclude that, the Atangana-Baleanu operator is more effective and prominent biologically as compared to the Caputo derivative for the proposed problem. Design and analysis of a discrete method for a time-delayed reaction-diffusion epidemic model https://zbmath.org/1485.92143 2022-06-24T15:10:38.853281Z "Macías-Díaz, Jorge E." https://zbmath.org/authors/?q=ai:macias-diaz.jorge-eduardo "Ahmed, Nauman" https://zbmath.org/authors/?q=ai:ahmed.nauman "Jawaz, Muhammad" https://zbmath.org/authors/?q=ai:jawaz.muhammad "Rafiq, Muhammad" https://zbmath.org/authors/?q=ai:rafiq.muhammad-h "Rehman, Muhammad Aziz Ur" https://zbmath.org/authors/?q=ai:rehman.muhammad-aziz-ur In this paper, the authors first proposed a two-dimensional and time-delayed reaction-diffusion model to describe the propagation of infectious viral diseases like COVID-19, and then established the existence and stability of the equilibrium points. Moreover, the authors examined the bifurcation of this system in terms of one of the parameters. In particular, they developed a time-splitting nonlocal finite-difference scheme to simulate numerically this mathematical model. Reviewer: Jia-Bing Wang (Wuhan) Dynamical analysis and control strategies in modelling Ebola virus disease https://zbmath.org/1485.92144 2022-06-24T15:10:38.853281Z "Mhlanga, A." https://zbmath.org/authors/?q=ai:mhlanga.a Summary: Ebola virus disease (EVD) is a severe infection with an extremely high fatality rate spread through direct and indirect contacts. Recently, an outbreak of EVD in West Africa brought public attention to this deadly disease. We study the spread of EVD through a two-patch model. We determine the basic reproduction number, the disease-free equilibrium, two boundary equilibria and the endemic equilibrium when the disease persists in the two sub-populations for specific conditions. Further, we introduce time-dependent controls into our proposed model. We analyse the optimal control problem where the control system is a mathematical model for EVD that incorporates educational campaigns. The control functions represent educational campaigns in their respective patches, with one patch having more effective controls than the other. We aim to study how these control measures would be implemented for a certain time period, in order to reduce or eliminate EVD in the respective communities, while minimising the intervention implementation costs. Numerical simulations results are provided to illustrate the dynamics of the disease in the presence of controls. The heterogeneous severity of COVID-19 in african countries: a modeling approach https://zbmath.org/1485.92145 2022-06-24T15:10:38.853281Z "Musa, Salihu Sabiu" https://zbmath.org/authors/?q=ai:musa.salihu-sabiu "Wang, Xueying" https://zbmath.org/authors/?q=ai:wang.xueying "Zhao, Shi" https://zbmath.org/authors/?q=ai:zhao.shi "Li, Shudong" https://zbmath.org/authors/?q=ai:li.shudong "Hussaini, Nafiu" https://zbmath.org/authors/?q=ai:hussaini.nafiu "Wang, Weiming" https://zbmath.org/authors/?q=ai:wang.weiming "He, Daihai" https://zbmath.org/authors/?q=ai:he.daihai Summary: The COVID-19 pandemic has had a considerable impact on global health and economics. The impact in African countries has not been investigated thoroughly via fitting epidemic models to the reported COVID-19 deaths. We downloaded the data for the 12 most-affected countries with the highest cumulative COVID-19 deaths to estimate the time-varying basic reproductive number $$({R}_0(t))$$ and infection attack rate. We develop a simple epidemic model and fitted it to reported COVID-19 deaths in 12 African countries using iterated filtering and allowing a flexible transmission rate. We observe high heterogeneity in the case-fatality rate across the countries, which may be due to different reporting or testing efforts. South Africa, Tunisia, and Libya were most affected, exhibiting a relatively higher $${R}_0(t)$$ and infection attack rate. Thus, to effectively control the spread of COVID-19 epidemics in Africa, there is a need to consider other mitigation strategies (such as improvements in socioeconomic well-being, healthcare systems, the water supply, and awareness campaigns). Ergodicity and extinction in a stochastic susceptible-infected-recovered-susceptible epidemic model with influence of information https://zbmath.org/1485.92146 2022-06-24T15:10:38.853281Z "Mu, Xiaojie" https://zbmath.org/authors/?q=ai:mu.xiaojie "Zhang, Qimin" https://zbmath.org/authors/?q=ai:zhang.qimin "Wu, Han" https://zbmath.org/authors/?q=ai:wu.han "Li, Xining" https://zbmath.org/authors/?q=ai:li.xining Summary: An epidemic model with stochastic contact transmission coefficient takes into account white noise and the influence of information. Sufficient conditions for the extinction and persistence of the disease are expressed. The existence of a stationary distribution and the ergodic property are proved. The peak of infected population can be decreased by information. The analytical results are showed by simulations and the influence of white noise and information on the dynamics of epidemics are evaluated. Global stability of SAIRS epidemic models https://zbmath.org/1485.92147 2022-06-24T15:10:38.853281Z "Ottaviano, Stefania" https://zbmath.org/authors/?q=ai:ottaviano.stefania "Sensi, Mattia" https://zbmath.org/authors/?q=ai:sensi.mattia "Sottile, Sara" https://zbmath.org/authors/?q=ai:sottile.sara Summary: We study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission patterns of the disease. We provide a global stability analysis for the model. We determine the value of the basic reproduction number $$\mathcal{R}_0$$ and prove that the disease-free equilibrium is globally asymptotically stable if $$\mathcal{R}_0 < 1$$. If $$\mathcal{R}_0 > 1$$, the disease free equilibrium is unstable and a unique endemic equilibrium exists. We investigate the global stability of the endemic equilibrium for some variations of the original model under study and answer an open problem proposed in [\textit{S. Ansumali} et al., Modelling a pandemic with asymptomatic patients, impact of lockdown and herd immunity, with applications to SARS-CoV-2'', Ann. rev. Control 50, 432--447 (2020; \url{doi:10.1016/j.arcontrol.2020.10.003})]. In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when $$\mathcal{R}_0 = 1$$. We provide a thorough numerical exploration of our model to illustrate our analytical results. A fractional order approach to modeling and simulations of the novel COVID-19 https://zbmath.org/1485.92148 2022-06-24T15:10:38.853281Z "Owusu-Mensah, Isaac" https://zbmath.org/authors/?q=ai:mensah.isaac-owusu "Akinyemi, Lanre" https://zbmath.org/authors/?q=ai:akinyemi.lanre "Oduro, Bismark" https://zbmath.org/authors/?q=ai:oduro.bismark "Iyiola, Olaniyi S." https://zbmath.org/authors/?q=ai:iyiola.olaniyi-samuel Summary: The novel coronavirus (SARS-CoV-2), or COVID-19, has emerged and spread at fast speed globally; the disease has become an unprecedented threat to public health worldwide. It is one of the greatest public health challenges in modern times, with no proven cure or vaccine. In this paper, our focus is on a fractional order approach to modeling and simulations of the novel COVID-19. We introduce a fractional type susceptible-exposed-infected-recovered (SEIR) model to gain insight into the ongoing pandemic. Our proposed model incorporates transmission rate, testing rates, and transition rate (from asymptomatic to symptomatic population groups) for a holistic study of the coronavirus disease. The impacts of these parameters on the dynamics of the solution profiles for the disease are simulated and discussed in detail. Furthermore, across all the different parameters, the effects of the fractional order derivative are also simulated and discussed in detail. Various simulations carried out enable us gain deep insights into the dynamics of the spread of COVID-19. The simulation results confirm that fractional calculus is an appropriate tool in modeling the spread of a complex infectious disease such as the novel COVID-19. In the absence of vaccine and treatment, our analysis strongly supports the significance reduction in the transmission rate as a valuable strategy to curb the spread of the virus. Our results suggest that tracing and moving testing up has an important benefit. It reduces the number of infected individuals in the general public and thereby reduces the spread of the pandemic. Once the infected individuals are identified and isolated, the interaction between susceptible and infected individuals diminishes and transmission reduces. Furthermore, aggressive testing is also highly recommended. Nonlinear control of infection spread based on a deterministic SEIR model https://zbmath.org/1485.92149 2022-06-24T15:10:38.853281Z "Piccirillo, Vinicius" https://zbmath.org/authors/?q=ai:piccirillo.vinicius Summary: In this study, a mathematical model (SEIR model) with a restriction parameter is used to explore the dynamic of the COVID-19 pandemic. This work presents a nonlinear and robust control algorithm based on variable structure control (VSC) to control the transmission of coronavirus disease (COVID-19). The VSC algorithm is a control gain switching technique in which is necessary to define a switching surface. Three switching surfaces are proposed based on rules that depend on: (i) exposed and infected population, (ii) susceptible and infected population, and (iii) susceptible and total population. In case (iii) a model-based state estimator is presented based on the extended Kalman filter (EKF) and the estimator is used in combination with the VSC. Numerical results demonstrate that the proposed control strategies have the ability to flatten the infection curve. In addition, the simulations show that the success of lowering and flattening the epidemic peak is strongly dependent on the chosen switching surfaces. A comparison between the VSC and sliding mode control (SMC) is presented showing that the VSC control can provide better performance taking into account two aspects: time duration of pandemic and the flattened curve peak with respect to SMC. Dynamics in a simple evolutionary-epidemiological model for the evolution of an initial asymptomatic infection stage https://zbmath.org/1485.92150 2022-06-24T15:10:38.853281Z "Saad-Roy, Chadi M." https://zbmath.org/authors/?q=ai:saad-roy.chadi-m "Wingreen, Ned S." https://zbmath.org/authors/?q=ai:wingreen.ned-s "Grenfell, Bryan T." https://zbmath.org/authors/?q=ai:grenfell.bryan-t Summary: Pathogens exhibit a rich variety of life history strategies, shaped by natural selection. An important pathogen life history characteristic is the propensity to induce an asymptomatic yet productive (transmissive) stage at the beginning of an infection. This characteristic is subject to complex trade-offs, ranging from immunological considerations to population-level social processes. We aim to classify the evolutionary dynamics of such asymptomatic behavior of pathogens (hereafter latency'') in order to unify epidemiology and evolution for this life history strategy. We focus on a simple epidemiological model with two infectious stages, where hosts in the first stage can be partially or fully asymptomatic. Immunologically, there is a trade-off between transmission and progression in this first stage. For arbitrary trade-offs, we derive different conditions that guarantee either at least one evolutionarily stable strategy (ESS) at zero, some, or maximal latency of the first stage or, perhaps surprisingly, at least one unstable evolutionarily singular strategy. In this latter case, there is bistability between zero and nonzero (possibly maximal) latency. We then prove the uniqueness of interior evolutionarily singular strategies for power-law and exponential trade-offs: Thus, bistability is always between zero and maximal latency. Overall, previous multistage infection models can be summarized with a single model that includes evolutionary processes acting on latency. Since small changes in parameter values can lead to abrupt transitions in evolutionary dynamics, appropriate disease control strategies could have a substantial impact on the evolution of first-stage latency. Optimal control model for blindness due to deficiency of vitamin A https://zbmath.org/1485.92151 2022-06-24T15:10:38.853281Z "Shah, Nita H." https://zbmath.org/authors/?q=ai:shah.nita-h "Yeolekar, Bijal M." https://zbmath.org/authors/?q=ai:yeolekar.bijal-m "Patel, Zalak A." https://zbmath.org/authors/?q=ai:patel.zalak-a Summary: Blindness is diminishing of optical ability to see. It is due to damage in some portion of eye, optical nerve and the core area of mind responsible for visualisation. The main cause of blindness is deficiency of vitamin A in an individual. Many prevention programmes are organized worldwide to control the blindness. The non-linear mathematical model is formulated with the relation between three compartments viz. healthy, vitamin A deficiency and blind individual in the population. Two conflicted controls for optimization of the model are discussed. On one hand, increasing the consumption of vitamin A in the deceased decreases the treatment and complaining for blind people on the other side in the society. The basic reproduction number is calculated to see the epidemic behavior of the model. The stability analysis is carried out. We optimize model with maximize consumption of vitamin A to minimize the blindness. The maxmin-criteria is used for optimal controls which are functions of time. Numerical simulation and analysis support the analytical results for optimal control in the model. A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control https://zbmath.org/1485.92152 2022-06-24T15:10:38.853281Z "Shaikh, Amjad Salim" https://zbmath.org/authors/?q=ai:shaikh.amjad-salim "Shaikh, Iqbal Najiroddin" https://zbmath.org/authors/?q=ai:shaikh.iqbal-najiroddin "Nisar, Kottakkaran Sooppy" https://zbmath.org/authors/?q=ai:sooppy-nisar.kottakkaran Summary: Since the first case of 2019 novel coronavirus disease (COVID-19) detected on 30 January, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April, 2020. Taking this into account, in the present work, we have analysed a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual response and control measures by the government. The real data available about number of infected cases from 14 March, 2000 to 26 March, 2020 is analysed and, accordingly, various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Further, we conduct stability analysis for both disease-free and endemic equilibrium states. On the basis of sensitivity analysis and dynamics of the threshold parameter, we estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies of the disease using the proposed model. Numerical computations are carried out utilising the iterative Laplace transform method and comparative study of different fractional differential operators is done. The impacts of various biological parameters on transmission dynamics of COVID-19 is investigated. Finally, we illustrate the obtained results graphically. Analysis of an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on delta-notch pathway https://zbmath.org/1485.92153 2022-06-24T15:10:38.853281Z "Sun, Deshun" https://zbmath.org/authors/?q=ai:sun.deshun "Lu, Lingyun" https://zbmath.org/authors/?q=ai:lu.lingyun "Liu, Fei" https://zbmath.org/authors/?q=ai:liu.fei.1|liu.fei.2|liu.fei "Duan, Li" https://zbmath.org/authors/?q=ai:duan.li "Wang, Daping" https://zbmath.org/authors/?q=ai:wang.daping "Xiong, Jianyi" https://zbmath.org/authors/?q=ai:xiong.jianyi Summary: In this paper, an improved fractional-order model of boundary formation in the \textit{Drosophila} large intestine dependent on Delta-Notch pathway is proposed for the first time. The uniqueness, nonnegativity, and boundedness of solutions are studied. In a two cells model, there are two equilibriums (no-expression of Delta and normal expression of Delta). Local asymptotic stability is proved for both cases. Stability analysis shows that the orders of the fractional-order differential equation model can significantly affect the equilibriums in the two cells model. Numerical simulations are presented to illustrate the conclusions. Next, the sensitivity of model parameters is calculated, and the calculation results show that different parameters have different sensitivities. The most and least sensitive parameters in the two cells model and the 60 cells model are verified by numerical simulations. What is more, we compare the fractional-order model with the integer-order model by simulations, and the results show that the orders can significantly affect the dynamic and the phenotypes. Transmission dynamics of cholera: mathematical modeling and control strategies https://zbmath.org/1485.92154 2022-06-24T15:10:38.853281Z "Sun, Gui-Quan" https://zbmath.org/authors/?q=ai:sun.guiquan "Xie, Jun-Hui" https://zbmath.org/authors/?q=ai:xie.junhui "Huang, Sheng-He" https://zbmath.org/authors/?q=ai:huang.sheng-he "Jin, Zhen" https://zbmath.org/authors/?q=ai:jin.zhen "Li, Ming-Tao" https://zbmath.org/authors/?q=ai:li.mingtao "Liu, Liqun" https://zbmath.org/authors/?q=ai:liu.liqun Summary: Cholera, as an endemic disease around the world, has generated great threat to human society and caused enormous morbidity and mortality with weak surveillance system. In this paper, we propose a mathematical model to describe the transmission of Cholera. Moreover, basic reproduction number and the global dynamics of the dynamical model are obtained. Then we apply our model to characterize the transmission process of Cholera in China. It was found that, in order to avoid its outbreak in China, it may be better to increase immunization coverage rate and make effort to improve environmental management especially for drinking water. Our results may provide some new insights for elimination of Cholera. Host-pathogen interaction for larvae oysters with salinity dependent transmission https://zbmath.org/1485.92155 2022-06-24T15:10:38.853281Z "Sunthawanic, Kalanyu" https://zbmath.org/authors/?q=ai:sunthawanic.kalanyu "Bunwong, Kornkanok" https://zbmath.org/authors/?q=ai:bunwong.kornkanok "Sae-jie, Wichuta" https://zbmath.org/authors/?q=ai:sae-jie.wichuta Summary: Mathematical models of host-pathogen interactions are proposed and analyzed. Here hosts are oyster population in a free-swimming larval stage and assumably live in the closed homogeneous environment. In terms of an epidemic, they are classified into two states, namely susceptible and infectious hosts. The epidemic model of oyster hosts with seasonal forced transmission is firstly described by the SIS model where the region of attraction, the existence of equilibrium points, their stability conditions, and upper and lower bounds on the attack rate are investigated. Then free-living pathogen is introduced in the oyster area. Numerical simulations are finally carried out by making use of the various salinity-dependent transmissions in support of the hypothesis that the lower the salinity level, the lower oyster's immunity. Effects of sterile males and fertility of infected mosquitoes on mosquito-borne disease dynamics https://zbmath.org/1485.92156 2022-06-24T15:10:38.853281Z "Sun, Xiaoli" https://zbmath.org/authors/?q=ai:sun.xiaoli "Liu, Shengqiang" https://zbmath.org/authors/?q=ai:liu.shengqiang "Lv, Yunfei" https://zbmath.org/authors/?q=ai:lv.yunfei "Pei, Yongzhen" https://zbmath.org/authors/?q=ai:pei.yongzhen Summary: By studying an infection-age structured model, we consider the effects of releasing sterile males and the fertility of infected mosquitoes on the mosquito-borne diseases transmission including the extinction of mosquitoes, the elimination and persistence of diseases. Firstly, equivalent integral equations are established to prove the well-posedness of solutions. Then, the main results of disease dynamics are given. By taking chikungunya as a numerical simulation example, an optimal releasing threshold is given according to our presupposed control standard. When the fertility disturbance of infected mosquitoes is small, the high releasing amount plays a main role on the control of the disease; however, when the fertility disturbance is large, the initial distributions and the fertility of infected mosquitoes are the key factors to control the disease. Mathematically, the fertility of infected mosquitoes makes the system have complex dynamics with multiple positive equilibria and bistability. On the nonstandard numerical discretization of SIR epidemic model with a saturated incidence rate and vaccination https://zbmath.org/1485.92157 2022-06-24T15:10:38.853281Z "Suryanto, Agus" https://zbmath.org/authors/?q=ai:suryanto.agus "Darti, Isnani" https://zbmath.org/authors/?q=ai:darti.isnani Summary: Recently, \textit{M. T. Hoang} and \textit{O. F. Egbelowo} [Bol. Soc. Mat. Mex., III. Ser. 26, No. 3, 1113--1134 (2020; Zbl 1455.92133)] proposed a nonstandard finite difference scheme (NSFD) to get a discrete SIR epidemic model with saturated incidence rate and constant vaccination. The discrete model was derived by discretizing the right-hand sides of the system locally and the first order derivative is approximated by the generalized forward difference method but with a restrictive denominator function. Their analysis showed that the NSFD scheme is dynamically-consistent only for relatively small time-step sizes. In this paper, we propose and analyze an alternative NSFD scheme by applying nonlocal approximation and choosing the denominator function such that the proposed scheme preserves the boundedness of solutions. It is verified that the proposed discrete model is dynamically-consistent with the corresponding continuous model for all time-step size. The analytical results have been confirmed by some numerical simulations. We also show numerically that the proposed NSFD scheme is superior to the Euler method and the NSFD method proposed by Hoang and Egbelowo [loc. cit.]. Cost effective reproduction number based strategies for reducing deaths from COVID-19 https://zbmath.org/1485.92158 2022-06-24T15:10:38.853281Z "Thron, Christopher" https://zbmath.org/authors/?q=ai:thron.christopher-penniman "Mbazumutima, Vianney" https://zbmath.org/authors/?q=ai:mbazumutima.vianney "Tamayo, Luis V." https://zbmath.org/authors/?q=ai:tamayo.luis-v "Todjihounde, Léonard" https://zbmath.org/authors/?q=ai:todjihounde.leonard Summary: In epidemiology, the effective reproduction number $$R_e$$ is used to characterize the growth rate of an epidemic outbreak. If $$R_e >1$$, the epidemic worsens, and if $$R_e< 1$$, then it subsides and eventually dies out. In this paper, we investigate properties of $$R_e$$ for a modified SEIR model of COVID-19 in the city of Houston, TX USA, in which the population is divided into low-risk and high-risk subpopulations. The response of $$R_e$$ to two types of control measures (testing and distancing) applied to the two different subpopulations is characterized. A nonlinear cost model is used for control measures, to include the effects of diminishing returns. Lowest-cost control combinations for reducing instantaneous $$R_e$$ to a given value are computed. We propose three types of heuristic strategies for mitigating COVID-19 that are targeted at reducing $$R_e$$, and we exhibit the tradeoffs between strategy implementation costs and number of deaths. We also consider two variants of each type of strategy: basic strategies, which consider only the effects of controls on $$R_e$$, without regard to subpopulation; and high-risk prioritizing strategies, which maximize control of the high-risk subpopulation. Results showed that of the three heuristic strategy types, the most cost-effective involved setting a target value for $$R_e$$ and applying sufficient controls to attain that target value. This heuristic led to strategies that begin with strict distancing of the entire population, later followed by increased testing. Strategies that maximize control on high-risk individuals were less cost-effective than basic strategies that emphasize reduction of the rate of spreading of the disease. The model shows that delaying the start of control measures past a certain point greatly worsens strategy outcomes. We conclude that the effective reproduction can be a valuable real-time indicator in determining cost-effective control strategies. A network-based explanation of why most COVID-19 infection curves are linear https://zbmath.org/1485.92159 2022-06-24T15:10:38.853281Z "Thurner, Stefan" https://zbmath.org/authors/?q=ai:thurner.stefan "Klimek, Peter" https://zbmath.org/authors/?q=ai:klimek.peter "Hanel, Rudolf" https://zbmath.org/authors/?q=ai:hanel.rudolf (no abstract) Reply to Kuśmierz and Toyoizumi: a network-based explanation of why most COVID-19 infection curves are linear https://zbmath.org/1485.92160 2022-06-24T15:10:38.853281Z "Thurner, Stefan" https://zbmath.org/authors/?q=ai:thurner.stefan "Klimek, Peter" https://zbmath.org/authors/?q=ai:klimek.peter "Hanel, Rudolf" https://zbmath.org/authors/?q=ai:hanel.rudolf Reply to [\textit{Ł. Kuśmierz} and \textit{T. Toyoizumi}, Proc. Natl. Acad. Sci. USA 118, No. 10, Paper No. e2024297118, 2 p. (2021; Zbl 1485.92137)]. Explicit formulae for the peak time of an epidemic from the SIR model https://zbmath.org/1485.92161 2022-06-24T15:10:38.853281Z "Turkyilmazoglu, Mustafa" https://zbmath.org/authors/?q=ai:turkyilmazoglu.mustafa Summary: Reducing the peak time of an epidemic disease in order for slowing down the eventual dynamics and getting prepared for the unavoidable epidemic wave is utmost significant to fight against the risks of a contagious epidemic disease. To serve to this purpose, the well-documented infection model of SIR is examined in the current research to propose an analytical approach for providing an explicit formula associated with a straightforward computation of peak time of outbreak. Initially, the time scale from the relevant autonomous SIR epidemic model is formulated analytically via an integral based on the fractions of susceptible and infected compartments. Afterwards, through a series expansion of the logarithmic term of the resultant integrand, the peak time is shown to rely upon the fraction of susceptible, the infectious ratio as well as the initial fractions of ill and susceptible individuals. The approximate expression is shown to rigorously capable of capturing the time threshold of illness for an epidemic from the semi-time SIR epidemiology. Otherwise, it is also successful to predict the peak time from a past history of a disease when all-time epidemic model is adopted. Accuracy of the derived expressions are initially confirmed by direct comparisons with recently reported approximate formulas in the literature. Several other epidemic disease samples including the COVID-19 often studied in the recent literature are eventually attacked with favourable performance of the presented formulae for assessing the peak time occurrence of an epidemic. A quick evaluation of the peak time of a disease certainly enables the governments to take early effective epidemic precautions. Study of transmission dynamics of novel COVID-19 by using mathematical model https://zbmath.org/1485.92162 2022-06-24T15:10:38.853281Z "Ud Din, Rahim" https://zbmath.org/authors/?q=ai:ud-din.rahim "Shah, Kamal" https://zbmath.org/authors/?q=ai:shah.kamal "Ahmad, Imtiaz" https://zbmath.org/authors/?q=ai:ahmad.imtiaz "Abdeljawad, Thabet" https://zbmath.org/authors/?q=ai:abdeljawad.thabet Summary: In this research work, we present a mathematical model for novel coronavirus-19 infectious disease which consists of three different compartments: susceptible, infected, and recovered under convex incident rate involving immigration rate. We first derive the formulation of the model. Also, we give some qualitative aspects for the model including existence of equilibriums and its stability results by using various tools of nonlinear analysis. Then, by means of the nonstandard finite difference scheme (NSFD), we simulate the results for the data of Wuhan city against two different sets of values of immigration parameter. By means of simulation, we show how protection, exposure, death, and cure rates affect the susceptible, infected, and recovered population with the passage of time involving immigration. On the basis of simulation, we observe the dynamical behavior due to immigration of susceptible and infected classes or one of these two. Dynamical behavior of stochastic SIRS model with two different incidence rates and Markovian switching https://zbmath.org/1485.92163 2022-06-24T15:10:38.853281Z "Wang, Feng" https://zbmath.org/authors/?q=ai:wang.feng.4|wang.feng.2|wang.feng.3|wang.feng.1 "Liu, Zaiming" https://zbmath.org/authors/?q=ai:liu.zaiming Summary: In this paper, we discuss SIRS models with two different incidence rates and Markovian switching. First, we consider that the parameters are perturbed by random environment modulated by Markovian switching. The segment method is used to prove that the model has a unique solution and the estimate of the solution is provided. The threshold values for determining extinction or persistence in mean of diseases are presented by theoretical analysis and some inequalities techniques. Furthermore, some results reveal that stochastic disturbances can suppress the disease outbreak. Because of regime switching, the diseases will be extinct (or persistent) although they might be persistent (or extinct) in some certain environments. Then, the model in which incidence rate functions are perturbed by random environment is also discussed and the values to judge the disease extinction are obtained. At last, a few examples are set to illustrate these interesting phenomena, and their simulations have been carried out to verify our theoretical outcomes. SVIR epidemic model with age structure in susceptibility, vaccination effects and relapse https://zbmath.org/1485.92164 2022-06-24T15:10:38.853281Z "Wang, Jinliang" https://zbmath.org/authors/?q=ai:wang.jinliang "Guo, Min" https://zbmath.org/authors/?q=ai:guo.min "Liu, Shengqiang" https://zbmath.org/authors/?q=ai:liu.shengqiang Summary: An SVIR epidemic model with continuous age structure in the susceptibility, vaccination effects and relapse is proposed. The asymptotic smoothness, existence of a global attractor, the stability of equilibria and persistence are addressed. It is shown that if the basic reproductive number $$\mathfrak{R}_0<1$$, then the disease-free equilibrium is globally asymptotically stable. If $$\mathfrak{R}_0>1$$, the disease is uniformly persistent, and a Lyapunov functional is used to show that the unique endemic equilibrium is globally asymptotically stable. Combined effects of susceptibility age, vaccination age and relapse age on the basic reproductive number are discussed. Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage https://zbmath.org/1485.92165 2022-06-24T15:10:38.853281Z "Wang, Xiaodong" https://zbmath.org/authors/?q=ai:wang.xiaodong.4|wang.xiaodong.6|wang.xiaodong|wang.xiaodong.5|wang.xiaodong.1 "Wang, Chunxia" https://zbmath.org/authors/?q=ai:wang.chunxia "Wang, Kai" https://zbmath.org/authors/?q=ai:wang.kai.3|wang.kai.2|wang.kai.4|wang.kai.1|wang.kai Summary: In this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $$R_0$$ which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results. Edge-based SEIR dynamics with or without infectious force in latent period on random networks https://zbmath.org/1485.92166 2022-06-24T15:10:38.853281Z "Wang, Yi" https://zbmath.org/authors/?q=ai:wang.yi.10|wang.yi.1|wang.yi.4|wang.yi.7|wang.yi.9|wang.yi.6|wang.yi.5|wang.yi.8|wang.yi.3 "Cao, Jinde" https://zbmath.org/authors/?q=ai:cao.jinde.1|cao.jinde "Alsaedi, Ahmed" https://zbmath.org/authors/?q=ai:alsaedi.ahmed "Ahmad, Bashir" https://zbmath.org/authors/?q=ai:ahmad.bashir.2 Summary: In nature, most of the diseases have latent periods, and most of the networks look as if they were spun randomly at the first glance. Hence, we consider SEIR dynamics with or without infectious force in latent period on random networks with arbitrary degree distributions. Both of these models are governed by intrinsically three dimensional nonlinear systems of ordinary differential equations, which are the same as classical SEIR models. The basic reproduction numbers and the final size formulae are explicitly derived. Predictions of the models agree well with the large-scale stochastic SEIR simulations on contact networks. In particular, for SEIR model without infectious force in latent period, although the length of latent period has no effect on the basic reproduction number and the final epidemic size, it affects the arrival time of the peak and the peak size; while for SEIR model with infectious force in latent period it also affects the basic reproduction number and the final epidemic size. These accurate model predictions, may provide guidance for the control of network infectious diseases with latent periods. Stochastic modeling of a mosquito-borne disease https://zbmath.org/1485.92167 2022-06-24T15:10:38.853281Z "Witbooi, Peter J." https://zbmath.org/authors/?q=ai:witbooi.peter-joseph "Abiodun, Gbenga J." https://zbmath.org/authors/?q=ai:abiodun.gbenga-jacob "van Schalkwyk, Garth J." https://zbmath.org/authors/?q=ai:van-schalkwyk.garth-j "Ahmed, Ibrahim H. I." https://zbmath.org/authors/?q=ai:ahmed.ibrahim-h-i Summary: We present and analyze a stochastic differential equation (SDE) model for the population dynamics of a mosquito-borne infectious disease. We prove the solutions to be almost surely positive and global. We introduce a numerical invariant $$\mathcal{R}$$ of the model with $$\mathcal{R}<1$$ being a condition guaranteeing the almost sure stability of the disease-free equilibrium. We show that stochastic perturbations enhance the stability of the disease-free equilibrium of the underlying deterministic model. We illustrate the main stability theorem through simulations and show how to obtain interval estimates when making forward projections. We consulted a wide range of literature to find relevant numerical parameter values. Evidence that coronavirus superspreading is fat-tailed https://zbmath.org/1485.92168 2022-06-24T15:10:38.853281Z "Wong, Felix" https://zbmath.org/authors/?q=ai:wong.felix-s "Collins, James J." https://zbmath.org/authors/?q=ai:collins.james-j Summary: Superspreaders, infected individuals who result in an outsized number of secondary cases, are believed to underlie a significant fraction of total SARS-CoV-2 transmission. Here, we combine empirical observations of SARS-CoV and SARS-CoV-2 transmission and extreme value statistics to show that the distribution of secondary cases is consistent with being fat-tailed, implying that large superspreading events are extremal, yet probable, occurrences. We integrate these results with interaction-based network models of disease transmission and show that superspreading, when it is fat-tailed, leads to pronounced transmission by increasing dispersion. Our findings indicate that large superspreading events should be the targets of interventions that minimize tail exposure. A note on advection-diffusion cholera model with bacterial hyperinfectivity https://zbmath.org/1485.92169 2022-06-24T15:10:38.853281Z "Wu, Xiaoqing" https://zbmath.org/authors/?q=ai:wu.xiaoqing "Shan, Yinghui" https://zbmath.org/authors/?q=ai:shan.yinghui "Gao, Jianguo" https://zbmath.org/authors/?q=ai:gao.jianguo In the recent paper by \textit{X. Wang} and \textit{F.-B. Wang} [J. Math. Anal. Appl. 480, No. 2, Article ID 123407, 29 p. (2019; Zbl 1423.92241)] a system of advection-diffusion equations was suggested to model the transmission of cholera. The authors complement these results proving two new theorems in the paper under review. Namely, Theorem 1.2 establishes local asymptotic stability and global attractivity of the cholera-free equilibrium $$E_{0}$$ for the case when the basic reproduction number $$\mathcal{R}_{0}=1.$$ For $$\mathcal{R}_{0}>1,$$ Theorem 1.3 furnishes sufficient conditions for global asymptotic stability of the positive equilibrium $$E^{\ast}.$$ Reviewer: Svitlana P. Rogovchenko (Kristiansand) Analysis of a multiscale HIV-1 model coupling within-host viral dynamics and between-host transmission dynamics https://zbmath.org/1485.92170 2022-06-24T15:10:38.853281Z "Xue, Yuyi" https://zbmath.org/authors/?q=ai:xue.yuyi "Xiao, Yanni" https://zbmath.org/authors/?q=ai:xiao.yanni The authors suggest a multiscale model for the spread of the human immunodeficiency virus (HIV) in the population. Single-scale models have been used in the literature for describing either the within-host viral dynamics at the individual level (microscale) or the between-host virus transmission at the population level (macroscale). In this paper, both types of dynamics are biderectionally coupled and a multiscale model consisting of six differential equations is suggested for describing the dynamics of the virus spread. The macroscale variables include the number of susceptibles $$S,$$ the number of HIV-positive individuals without clinical manifestation $$I,$$ and the number of AIDS patients with the progressing infection $$A.$$ The microscale variables $$T,$$ $$T^{\ast},$$ and $$V$$ stand for the densities of healthy T-cells, infected T-cells and viral load respectively. The multiscale system combines the dynamics on a fast scale within a host and a slow-scale dynamics between hosts. Dynamics of the fast subsystem is studied first and the existence of the unique positive globally asymptotically stable equilibrium is established in Theorem 1. Then the analysis of the slow subsystem is conducted. A criterion for the local asymptotic stability of the disease-free equilibrium of the slow system in terms of the basic reproductive number $$R_{s}$$ is given in Theorem 2. Theorem 3 provides conditions for the existence of positive equilibria for the slow subsystem and their number (no, one, or two equilibria). After this, local stability of the positive equilibrium is discussed. Numerical simulations are conducted to illustrate the occurrence of a backward bifurcation in the coupled system and the interplay between the slow and fast subsystems. The final section summarizes the main contributions made in the paper. Reviewer: Yuriy V. Rogovchenko (Kristiansand) Analysis of an age-structured HIV infection model with logistic target-cell growth and antiretroviral therapy https://zbmath.org/1485.92171 2022-06-24T15:10:38.853281Z "Yan, Dongxue" https://zbmath.org/authors/?q=ai:yan.dongxue "Fu, Xianlong" https://zbmath.org/authors/?q=ai:fu.xianlong Summary: This paper deals with the global dynamics of an age-structured human immunodeficiency virus infection model which incorporates a logistic growth term for the target cells and antiretroviral therapy. We perform some rigourous analyses for the model, including presenting an explicit formula for the reproductive number of the model, addressing the persistence of the solution semi-flow and the existence of a global attractor. Based on these analyses we establish some results on stability and instability for the system. The existence of Hopf bifurcation is also obtained around the positive equilibrium. Finally, some numerical examples are provided to illustrate our obtained results. Dynamics of a delayed SIR model for the transmission of PRRSV among a swine population https://zbmath.org/1485.92172 2022-06-24T15:10:38.853281Z "Zou, Junchen" https://zbmath.org/authors/?q=ai:zou.junchen "Upadhyay, Ranjit Kumar" https://zbmath.org/authors/?q=ai:kumar-upadhyay.ranjit "Pratap, A." https://zbmath.org/authors/?q=ai:pratap.anbalagan|pratap.amrit|pratap.ajay "Zhang, Zizhen" https://zbmath.org/authors/?q=ai:zhang.zizhen Summary: The objective of this paper is to propose a delayed susceptible-infectious-recovered (SIR) model for the transmission of porcine reproductive respiratory syndrome virus (PRRSV) among a swine population, including the latent period delay of the virus and the time delay due to the period the infectious swines need to recover. By taking different combinations of the two delays as the bifurcation parameter, local stability of the disease-present equilibrium and the existence of Hopf bifurcation are analyzed. Sufficient conditions for global stability of the disease-present equilibrium are derived by constructing a suitable Lyapunov function. Directly afterwards, properties of the Hopf bifurcation such as direction and stability are studied with the aid of the normal form theory and center manifold theorem. Finally, numerical simulations are presented to justify the validity of the derived theoretical results. Modeling and simulation of air pollutant distribution in street canyon area with Skytrain stations https://zbmath.org/1485.92173 2022-06-24T15:10:38.853281Z "Chomcheon, Suranath" https://zbmath.org/authors/?q=ai:chomcheon.suranath "Khajohnsaksumeth, Nathnarong" https://zbmath.org/authors/?q=ai:khajohnsaksumeth.nathnarong "Wiwatanapataphee, Benchawan" https://zbmath.org/authors/?q=ai:wiwatanapataphee.benchawan "Ge, Xiangyu" https://zbmath.org/authors/?q=ai:ge.xiangyu Summary: This paper focuses on effects of the wind flow velocity on the air flow and the air pollution dispersion in a street canyon with Skytrain. The governing equations of air pollutants and air flow in this study area are the convection-diffusion equations of species concentration and the Reynolds-averaged Navier-Stokes (RANS) equations of compressible turbulent flow, respectively. Finite element method is utilized for the solution of the problem. To investigate the impact of the air flow on the pattern of air pollution dispersion, three speeds of inlet wind in three different blowing directions are chosen. The results illustrate that our model can depict the airflows and dispersion patterns for different wind conditions. Effects of precipitation intermittency on vegetation patterns in semi-arid landscapes https://zbmath.org/1485.92174 2022-06-24T15:10:38.853281Z "Eigentler, L." https://zbmath.org/authors/?q=ai:eigentler.lukas "Sherratt, J. A." https://zbmath.org/authors/?q=ai:sherratt.jonathan-a Summary: Patterns of vegetation are a characteristic feature of many semi-arid regions. The limiting resource in these ecosystems is water, which is added to the system through short and intense rainfall events that cause a pulse of biological processes such as plant growth and seed dispersal. We propose an impulsive model based on the Klausmeier reaction-advection-diffusion system, analytically investigate the effects of rainfall intermittency on the onset of patterns, and augment our results by numerical simulations of model extensions. Our investigation focuses on the parameter region in which a transition between uniform and patterned vegetation occurs. Results show that decay-type processes associated with a low frequency of precipitation pulses inhibit the onset of patterns and that under intermittent rainfall regimes, a spatially uniform solution is sustained at lower total precipitation volumes than under continuous rainfall, if plant species are unable to efficiently use low soil moisture levels. Unlike in the classical setting of a reaction-diffusion model, patterns are not caused by a diffusion-driven instability but by a combination of sufficiently long periods of droughts between precipitation pulses and water diffusion. Our results further indicate that the introduction of pulse-type seed dispersal weakens the effects of changes to width and shape of the plant dispersal kernel on the onset of patterns. A Fisher-KPP model with a nonlocal weighted free boundary: analysis of how habitat boundaries expand, balance or shrink https://zbmath.org/1485.92175 2022-06-24T15:10:38.853281Z "Feng, Chunxi" https://zbmath.org/authors/?q=ai:feng.chunxi "Lewis, Mark A." https://zbmath.org/authors/?q=ai:lewis.mark-a "Wang, Chuncheng" https://zbmath.org/authors/?q=ai:wang.chuncheng "Wang, Hao" https://zbmath.org/authors/?q=ai:wang.hao.4 Summary: In this paper, we propose a novel free boundary problem to model the movement of single species with a range boundary. The spatial movement and birth/death processes of the species found within the range boundary are assumed to be governed by the classic Fisher-KPP reaction-diffusion equation, while the movement of a free boundary describing the range limit is assumed to be influenced by the weighted total population inside the range boundary and is described by an integro-differential equation. Our free boundary equation is a generalization of the classical Stefan problem that allows for nonlocal influences on the boundary movement so that range expansion and shrinkage are both possible. In this paper, we prove that the new model is well-posed and possesses steady state. We show that the spreading speed of the range boundary is smaller than that for the equivalent problem with a Stefan condition. This implies that the nonlocal effect of the weighted total population on the boundary movement slows down the spreading speed of the population. While the classical Stefan condition categorizes asymptotic behavior via a spreading-vanishing dichotomy, the new model extends this dichotomy to a spreading-balancing-vanishing trichotomy. We specifically analyze how habitat boundaries expand, balance or shrink. When the model is extended to have two free boundaries, we observe the steady state scenario, asymmetric shifts, or even boundaries moving synchronously in the same direction. These are newly discovered phenomena in the free boundary problems for animal movement. Survival analysis of a stochastic cooperation system with functional response in a polluted environment https://zbmath.org/1485.92176 2022-06-24T15:10:38.853281Z "Guo, Shengliang" https://zbmath.org/authors/?q=ai:guo.shengliang Summary: In this paper, we propose and study a stochastic two-species cooperation model with functional response in a polluted environment. We first perform the survival analysis and establish sufficient conditions for extinction, weak persistence, and stochastic permanence. Then we further perform the survival analysis based on the temporal average of population size and derive sufficient conditions for the strong persistence in the mean and weak persistence in the mean. Finally, we present numerical simulations to justify the theoretical results. The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation https://zbmath.org/1485.92177 2022-06-24T15:10:38.853281Z "Jaïbi, Olfa" https://zbmath.org/authors/?q=ai:jaibi.olfa "Doelman, Arjen" https://zbmath.org/authors/?q=ai:doelman.arjen "Chirilus-Bruckner, Martina" https://zbmath.org/authors/?q=ai:chirilus-bruckner.martina "Meron, Ehud" https://zbmath.org/authors/?q=ai:meron.ehud Summary: In this paper we consider the 2-component reaction-diffusion model that was recently obtained by a systematic reduction of the 3-component Gilad et al. model for dryland ecosystem dynamics \textit{E. Gilad} et al. [Ecosystem engineers: from pattern formation to habitat creation'', Phys. Rev. Lett. 93, No. 9, Article ID 098105, 4 p. (2004; \url{doi:10.1103/PhysRevLett.93.098105})]. The nonlinear structure of this model is more involved than other more conceptual models, such as the extended \textit{C. A. Klausmeier} [Regular and irregular patterns in semiarid vegetation'', Science 284, No. 5421, 1826--1828 (1999; \url{doi:10.1126/science.284.5421.1826})] model, and the analysis a priori is more complicated. However, the present model has a strong advantage over these more conceptual models in that it can be more directly linked to ecological mechanisms and observations. Moreover, we find that the model exhibits a richness of analytically tractable patterns that exceeds that of Klausmeier-type models. Our study focuses on the 4-dimensional dynamical system associated with the reaction-diffusion model by considering traveling waves in 1 spatial dimension. We use the methods of geometric singular perturbation theory to establish the existence of a multitude of heteroclinic/homoclinic/periodic orbits that `jump' between (normally hyperbolic) slow manifolds, representing various kinds of localized vegetation patterns. The basic 1-front invasion patterns and 2-front spot/gap patterns that form the starting point of our analysis have a direct ecological interpretation and appear naturally in simulations of the model. By exploiting the rich nonlinear structure of the model, we construct many multi-front patterns that are novel, both from the ecological and the mathematical point of view. In fact, we argue that these orbits/patterns are not specific for the model considered here, but will also occur in a much more general (singularly perturbed reaction-diffusion) setting. We conclude with a discussion of the ecological and mathematical implications of our findings. A non-autonomous impulsive food-chain model with delays https://zbmath.org/1485.92178 2022-06-24T15:10:38.853281Z "Tian, Baodan" https://zbmath.org/authors/?q=ai:tian.baodan "Zhang, Pengkai" https://zbmath.org/authors/?q=ai:zhang.pengkai "Li, Jiamei" https://zbmath.org/authors/?q=ai:li.jiamei "Zhang, Yong" https://zbmath.org/authors/?q=ai:zhang.yong.14|zhang.yong|zhang.yong.1|zhang.yong.13|zhang.yong.2|zhang.yong.4|zhang.yong.8|zhang.yong.7|zhang.yong.5|zhang.yong.11|zhang.yong.10|zhang.yong.15|zhang.yong.9|zhang.yong.12 "Yang, Liu" https://zbmath.org/authors/?q=ai:yang.liu.4 Summary: A non-autonomous almost periodic prey-predator system with impulsive effects and multiple delays is proposed in this paper, Holling's-type-IV systems and ratio-dependent functional responses are also involved in the model. By applying absolute inequalities, integral inequalities, differential inequalities and the mean-value theorem and other mathematical analysis techniques, we obtain some sufficient conditions which guarantee the permanence of the system. Moreover, we obtain the existence and the uniqueness of the almost periodic solution which is uniformly asymptotically stable by constructing a series of Lyapunov functionals. Finally, we present several numerical examples to verify the theoretical results and present some discussions of pest management in the agricultural ecological system. Investigation of an explosive food chain model with interference and inhibitory effects https://zbmath.org/1485.92179 2022-06-24T15:10:38.853281Z "Upadhyay, Ranjit Kumar" https://zbmath.org/authors/?q=ai:kumar-upadhyay.ranjit "Mishra, Swati" https://zbmath.org/authors/?q=ai:mishra.swati "Parshad, Rana D." https://zbmath.org/authors/?q=ai:parshad.rana-d "Lyu, Jingjing" https://zbmath.org/authors/?q=ai:lyu.jingjing "Basheer, Aladeen Al" https://zbmath.org/authors/?q=ai:al-basheer.aladeen Summary: In the current manuscript, we have investigated the temporal as well as spatio-temporal dynamics of a three species modified Leslie-Gower food chain model with Holling type IV and Crowley-Martin function responses. We have shown that explosion in the top predator population can be prevented if group defence is sufficiently strong at the lowest trophic levels. This demonstrates that group defence can act as a damping mechanism, and prevent population explosion of apex predators. We also show that the spatially explicit model can exhibit diffusion-driven instability, that depends strongly on the intensity of the group defence, in the prey population. Standard bifurcation analysis and the period doubling route to chaos are also investigated. Hopf bifurcation controlling for a fractional order delayed paddy ecosystem in the fallow season https://zbmath.org/1485.92180 2022-06-24T15:10:38.853281Z "Zheng, Kun" https://zbmath.org/authors/?q=ai:zheng.kun "Zhou, Xiaoli" https://zbmath.org/authors/?q=ai:zhou.xiaoli "Wu, Zhaohua" https://zbmath.org/authors/?q=ai:wu.zhaohua "Wang, Zhiming" https://zbmath.org/authors/?q=ai:wang.zhiming "Zhou, Tiejun" https://zbmath.org/authors/?q=ai:zhou.tiejun Summary: Since bifurcation makes it difficult to manage a paddy ecosystem, controlling bifurcation is an important management tool. In this paper, the stability and bifurcation control for a fractional order paddy ecosystem in the fallow season with time delay are investigated. Firstly, a paddy ecosystem model formulated by two-dimensional delayed fractional order differential equations with linear delayed feedback controller is proposed to reveal the interaction between weeds and inorganic fertilizers in paddy systems. Using the time delay as the bifurcation parameter, the sufficient conditions for stability of the system and the existence of Hopf bifurcation are obtained by analyzing the relevant characteristic equations. The results show that the time delay can heavily affect the dynamics of the system, and the feedback gain and the fractional order have significant impact on the control effect. Finally, the verification of the accuracy and validity of these conclusions is made by two examples, the control effect of the feedback gain and the fractional order on Hopf bifurcation are illustrated intuitively by a contour map. Global solutions to multi-dimensional topological Euler alignment systems https://zbmath.org/1485.92181 2022-06-24T15:10:38.853281Z "Lear, Daniel" https://zbmath.org/authors/?q=ai:lear.daniel "Reynolds, David N." https://zbmath.org/authors/?q=ai:reynolds.david-n "Shvydkoy, Roman" https://zbmath.org/authors/?q=ai:shvydkoy.roman-v Summary: We present a systematic approach to regularity theory of the multi-dimensional Euler alignment systems with topological diffusion introduced in [the last author and \textit{E. Tadmor}, SIAM J. Math. Anal. 52, No. 6, 5792--5839 (2020; Zbl 1453.92371)]. While these systems exhibit flocking behavior emerging from purely local communication, bearing direct relevance to empirical field studies, global and even local well-posedness has proved to be a major challenge in multi-dimensional settings due to the presence of topological effects. In this paper we reveal two important classes of global smooth solutions -- parallel shear flocks with incompressible velocity and stationary density profile, and nearly aligned flocks with close to constant velocity field but arbitrary density distribution. Existence of such classes is established via an efficient continuation criterion requiring control only on the Lipschitz norm of state quantities, which makes it accessible to the applications of fractional parabolic theory. The criterion presents a major improvement over the existing result of [the second and the last author, Nonlinearity 33, No. 10, 5176--5214 (2020; Zbl 1451.92350)], and is proved with the use of quartic paraproduct estimates. A switching feedback control approach for persistence of managed resources https://zbmath.org/1485.93183 2022-06-24T15:10:38.853281Z "Franco, Daniel" https://zbmath.org/authors/?q=ai:franco-leis.daniel "Guiver, Chris" https://zbmath.org/authors/?q=ai:guiver.chris "Smith, Phoebe" https://zbmath.org/authors/?q=ai:smith.phoebe "Townley, Stuart" https://zbmath.org/authors/?q=ai:townley.stuart-b Summary: An adaptive switching feedback control scheme is proposed for classes of discrete-time, positive difference equations, or systems of equations. In overview, the objective is to choose a control strategy which ensures persistence of the state, consequently avoiding zero which corresponds to absence or extinction. A robust feedback control solution is proposed as the effects of different management actions are assumed to be uncertain. Our motivating application is to the conservation of dynamic resources, such as populations, which are naturally positive quantities and where discrete and distinct courses of management actions, or control strategies, are available. The theory is illustrated with examples from population ecology. Kalman 1960: the birth of modern system theory https://zbmath.org/1485.93217 2022-06-24T15:10:38.853281Z "Bernhard, Pierre" https://zbmath.org/authors/?q=ai:bernhard.pierre "Deschamps, Marc" https://zbmath.org/authors/?q=ai:deschamps.marc Summary: Rudolph E. Kalman is mainly known for the Kalman filter, first published in 1960. In this year, he published two equally important contributions, one about linear state space system theory and the other about linear quadratic optimal control theory. These three domains are intertwined in the later theory of linear quadratic Gaussian control. An extended version of linear quadratic optimal control is put into practice in an example of cooperation in population ecology. Mathematical modeling, forecasting, and optimal control of typhoid fever transmission dynamics https://zbmath.org/1485.93465 2022-06-24T15:10:38.853281Z "Abboubakar, Hamadjam" https://zbmath.org/authors/?q=ai:abboubakar.hamadjam "Racke, Reinhard" https://zbmath.org/authors/?q=ai:racke.reinhard Summary: In this paper, we derive and analyze a model for the control of typhoid fever which takes into account an imperfect vaccine combined with protection, environment sanitation, and treatment as control mechanisms. The analysis of the autonomous model passes through the computation of the control reproduction number $$\mathcal{R}_c$$, the proof of the local and global stability of the disease-free equilibrium whenever $$\mathcal{R}_c$$ is less than one using Lyapunov's theory. When $$\mathcal{R}_c$$ is greater than one, we prove the local asymptotic stability of the unique endemic equilibrium through the Center Manifold Theory and we find that the model exhibits a forward bifurcation. Using clinical data from Mbandjock, a town in the Centre Region of Cameroon, we calibrate the model by estimating model parameters. We find that the control reproduction number is approximatively equal to 2.4750, which means that we are in an endemic state $$(\mathcal{R}_c>1)$$. We also performed a sensitivity analysis by calculating the Partial Rank Correlation Coefficient (PRCC) of $$\mathcal{R}_c$$ and of infected compartments classes. Then, we extend the model by reformulating it as an optimal control problem, with the use of three time-dependent controls, namely vaccination, individual protection/environment sanitation, and treatment. Optimal control theory is used to analyze our optimal control model. Numerical simulations and efficiency analysis are performed to show the impact of each control strategy on the decrease of the disease burden.