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## Thieme, Horst R.

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 Author ID: thieme.horst-r Published as: Thieme, H.; Thieme, H. R.; Thieme, Horst; Thieme, Horst R. Homepage: https://math.la.asu.edu/~thieme/ External Links: MGP · dblp · GND
 Documents Indexed: 140 Publications since 1977, including 6 Books
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#### Co-Authors

 45 single-authored 16 Smith, Hal Leslie 14 Diekmann, Odo 13 Gyllenberg, Mats 7 Heijmans, Henk J. A. M. 5 Clément, Philippe J. E. 5 Dhirasakdanon, Thanate 5 Martcheva, Maia 4 Castillo-Chavez, Carlos 4 Jin, Wen 3 Alanazi, Khalaf M. 3 Busenberg, Stavros N. 3 Cooke, Kenneth L. 3 Fan, Guihong 3 Farrell, Alex P. 3 Feng, Zhilan 3 Jackiewicz, Zdzislaw 3 Jones, Don A. 3 Kuang, Yang 3 Lant, Timothy 3 van den Driessche, Pauline 2 Ackleh, Azmy S. 2 Collins, James P. 2 Gourley, Stephen A. 2 Greer, Amy L. 2 Gwiazda, Piotr 2 Hadeler, Karl-Peter 2 Iannelli, Mimmo 2 Marciniak-Czochra, Anna K. 2 Metz, Johan A. Jacob 2 Röst, Gergely 2 Tridane, Abdessamad 2 Voigt, Jurgen 2 Vosseler, Hauke 2 Wu, Jianhong 2 Yang, Jinling 2 Zhao, Xiao-Qiang 1 Baer, Steven M. 1 Bremermann, Hans Joachim 1 Capasso, Vicenzo 1 Cleveland, John 1 Cumberbatch, Ellis 1 Dieckmann, O. 1 Dietz, Klaus 1 Faeth, Stanley H. 1 Fitzpatrick, Ben G. 1 Han, Zhun 1 Heesterbeek, J. A. P. 1 Hethcote, Herbert W. 1 Hillen, Thomas 1 Jennings, Rachel 1 Kooi, Bob W. 1 Kuznetsov, Yuri Alexandrovich 1 Lenhard, Suzanne 1 Lenhart, Suzanne M. 1 Lou, Yijun 1 Magal, Pierre 1 Martelli, Mario 1 Matsumoto, Toshitaka 1 Mischaikow, Konstantin 1 Mopecha, Jimmy P. 1 Navarova, Natalia 1 Oharu, Shinnosuke 1 Schuhmacher, K. 1 Tang, Betty K. P. 1 Trevino, Roy 1 Vrabie, Ioan I. 1 Wu, Xiaotian 1 Yakubu, Abdul-Aziz 1 Zhu, Huaiping
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#### Serials

 18 Journal of Mathematical Biology 8 SIAM Journal on Applied Mathematics 8 Discrete and Continuous Dynamical Systems. Series B 7 Mathematical Biosciences 6 Journal of Differential Equations 6 Differential and Integral Equations 5 SIAM Journal on Mathematical Analysis 4 Journal of Biological Dynamics 3 Journal of Mathematical Analysis and Applications 3 Journal of Dynamics and Differential Equations 3 Discrete and Continuous Dynamical Systems 3 Positivity 3 Natural Resource Modeling 2 Rocky Mountain Journal of Mathematics 2 Bulletin of Mathematical Biology 2 Journal für die Reine und Angewandte Mathematik 2 Manuscripta Mathematica 2 Semigroup Forum 2 Journal of Integral Equations 2 Advances in Mathematical Sciences and Applications 2 Mathematical Biosciences and Engineering 2 Mathematical Modelling of Natural Phenomena 1 Computers & Mathematics with Applications 1 Hiroshima Mathematical Journal 1 Mathematische Annalen 1 Mathematics and Computers in Simulation 1 Mathematische Zeitschrift 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Transactions of the American Mathematical Society 1 Applied Numerical Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Computers and Mathematics with Applications. Part A 1 The Canadian Applied Mathematics Quarterly 1 Electronic Journal of Differential Equations (EJDE) 1 Vietnam Journal of Mathematics 1 Nonlinear Analysis. Real World Applications 1 Journal of Evolution Equations 1 Communications on Pure and Applied Analysis 1 Graduate Studies in Mathematics 1 Networks and Heterogeneous Media
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#### Fields

 109 Biology and other natural sciences (92-XX) 47 Ordinary differential equations (34-XX) 46 Operator theory (47-XX) 30 Dynamical systems and ergodic theory (37-XX) 22 Integral equations (45-XX) 21 Partial differential equations (35-XX) 10 Probability theory and stochastic processes (60-XX) 5 Functional analysis (46-XX) 5 Systems theory; control (93-XX) 4 General and overarching topics; collections (00-XX) 4 Numerical analysis (65-XX) 3 Measure and integration (28-XX) 3 Difference and functional equations (39-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Statistics (62-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH Open

126 Publications have been cited 3,870 times in 2,543 Documents Cited by Year
Mathematics in population biology. Zbl 1054.92042
Thieme, Horst R.
2003
Persistence under relaxed point-dissipativity (with application to an endemic model). Zbl 0774.34030
Thieme, Horst R.
1993
Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations. Zbl 0761.34039
Thieme, Horst R.
1992
Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction–diffusion models. Zbl 1045.45009
Thieme, Horst R.; Zhao, Xiao-Qiang
2003
Dynamical systems and population persistence. Zbl 1214.37002
Smith, Hal L.; Thieme, Horst R.
2011
Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity. Zbl 1191.47089
Thieme, Horst R.
2009
Uniform persistence and permanence for non-autonomous semiflows in population biology. Zbl 0970.37061
Thieme, Horst R.
2000
Semiflows generated by Lipschitz perturbations of non-densely defined operators. Zbl 0734.34059
Thieme, Horst R.
1990
A competitive exclusion principle for pathogen virulence. Zbl 0715.92027
Bremermann, H. J.; Thieme, H. R.
1989
How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS? Zbl 0811.92021
Thieme, Horst R.; Castillo-Chavez, Carlos
1993
Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Zbl 0829.34037
Mischaikow, Konstantin; Smith, Hal; Thieme, Horst R.
1995
On the stability of the cell size distribution. Zbl 0543.92021
Diekmann, O.; Heijmans, H. J. A. M.; Thieme, H. R.
1984
On the formulation and analysis of general deterministic structured population models. I: Linear theory. Zbl 0909.92023
Diekmann, Odo; Gyllenberg, Mats; Metz, J. A. J.; Thieme, Horst R.
1998
“Integrated semigroups” and integrated solutions to abstract Cauchy problems. Zbl 0738.47037
Thieme, Horst R.
1990
Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations. Zbl 0395.45010
Thieme, Horst R.
1979
A non-local delayed and diffusive predator-prey model. Zbl 1113.92319
Thieme, Horst R.; Zhao, Xiao-Qiang
2001
Progression age enhanced backward bifurcation in an epidemic model with super-infection. Zbl 1097.92046
Martcheva, Maia; Thieme, Horst R.
2003
A model for the spatial spread of an epidemic. Zbl 0373.92031
Thieme, H. R.
1977
Stability of the endemic equilibrium in epidemic models with subpopulations. Zbl 0582.92024
Hethcote, Herbert W.; Thieme, Horst R.
1985
Global behavior of an age-structured epidemic model. Zbl 0741.92015
Busenberg, Stavros N.; Iannelli, Mimmo; Thieme, Horst R.
1991
Asymptotically autonomous differential equations in the plane. Zbl 0811.34036
Thieme, Horst R.
1994
Strongly order preserving semiflows generated by functional differential equations. Zbl 0735.34065
Smith, Hal L.; Thieme, Horst R.
1991
Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread. Zbl 0417.92022
Thieme, Horst R.
1979
Endemic models with arbitrarily distributed periods of infection. I: Fundamental properties of the model. Zbl 0991.92028
Feng, Zhilan; Thieme, Horst R.
2000
Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations. Zbl 0782.92018
Thieme, Horst R.
1992
Uniform weak implies uniform strong persistence for nonautonomous semiflows. Zbl 0918.34053
Thieme, Horst R.
1999
Recurrent outbreaks of childhood diseases revisited: The impact of isolation. Zbl 0833.92017
Feng, Zhilan; Thieme, Horst R.
1995
Convergence for strongly order-preserving semiflows. Zbl 0739.34040
Smith, Hal L.; Thieme, Horst R.
1991
Species decline and extinction: synergy of infectious disease and Allee effect? Zbl 1342.92206
Thieme, Horst R.; Dhirasakdanon, Thanate; Han, Zhun; Trevino, Roy
2009
Perturbation theory for dual semigroups. I. The sun-reflexive case. Zbl 0634.47039
Clément, Ph.; Diekmann, O.; Gyllenberg, M.; Heijmans, H. J. A. M.; Thieme, H. R.
1987
Quasi convergence and stability for strongly order-preserving semiflows. Zbl 0704.34054
Smith, Hal L.; Thieme, Horst R.
1990
Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators. Zbl 1215.37052
Thieme, Horst R.
2011
Quasi-compact semigroups via bounded perturbation. Zbl 0945.47033
Thieme, Horst R.
1997
Multiparametric bifurcation analysis of a basic two-stage population model. Zbl 1106.34030
Baer, S. M.; Kooi, B. W.; Kuznetsov, Yu. A.; Thieme, H. R.
2006
Eventual compactness for semiflows generated by nonlinear age-structured models. Zbl 1083.47061
Magal, P.; Thieme, H. R.
2004
Monotone semiflows in scalar non-quasi-monotone functional differential equations. Zbl 0719.34123
Smith, Hal L.; Thieme, Horst R.
1990
On the role of variable infectivity in the dynamics of the human immunodeficiency virus epidemic. Zbl 0687.92009
Thieme, Horst R.; Castillo-Chavez, Carlos
1989
Renewal theorems for linear periodic Volterra integral equations. Zbl 0566.45016
Thieme, Horst R.
1984
Endemic models with arbitrarily distributed periods of infection. II: Fast disease dynamics and permanent recovery. Zbl 1016.92035
Feng, Zhilan; Thieme, Horst R.
2000
Stable coexistence and bi-stability for competitive systems on ordered Banach spaces. Zbl 1064.47075
Smith, H. L.; Thieme, H. R.
2001
Well-posedness of physiologically structured population models for Daphnia magna. How biological concepts can benefit by abstract mathematical analysis. Zbl 0713.92020
Thieme, H. R.
1988
Rate distributions and survival of the fittest: a formulation on the space of measures. Zbl 1078.92055
Ackleh, Azmy S.; Fitzpatrick, Ben G.; Thieme, Horst R.
2005
Dynamics of an age structured epidemic model. Zbl 0943.92502
Busenberg, Stavros; Iannelli, Mimmo; Thieme, Horst
1993
Stability change of the endemic equilibrium in age-structured models for the spread of S-I-R type infectious diseases. Zbl 0748.92013
Thieme, Horst R.
1991
Perturbation theory for dual semigroups. II: Time-dependent perturbations in the sun-reflexive case. Zbl 0661.47015
Clément, Ph.; Diekmann, O.; Gyllenberg, M.; Heijmans, H. J. A. M.; Thieme, H. R.
1988
Delay differential systems for tick population dynamics. Zbl 1355.92087
Fan, Guihong; Thieme, Horst R.; Zhu, Huaiping
2015
Differentiability of convolutions, integrated semigroups of bounded semi-variation, and the inhomogeneous Cauchy problem. Zbl 1157.45007
Thieme, Horst R.
2008
Positive perturbation of operator semigroups: Growth bounds, essential compactness, and asynchronous exponential growth. Zbl 0988.47024
Thieme, Horst R.
1998
Demographic change and persistence of HIV/AIDS in a heterogeneous population. Zbl 0739.92014
Busenberg, Stavros; Cooke, Kenneth; Thieme, Horst
1991
Balanced exponential growth of operator semigroups. Zbl 0943.47032
Thieme, Horst R.
1998
Remarks on resolvent positive operators and their perturbation. Zbl 0962.47017
Thieme, Horst R.
1998
On a class of Hammerstein integral equations. Zbl 0417.45003
Thieme, Horst R.
1979
Stochastic semigroups: their construction by perturbation and approximation. Zbl 1113.47029
Thieme, H. R.; Voigt, J.
2006
Persistence of bacteria and phages in a chemostat. Zbl 1303.92123
Smith, Hal L.; Thieme, Horst R.
2012
Markov transition functions and semigroups of measures. Zbl 1146.47030
Lant, Timothy; Thieme, Horst R.
2007
Perturbing semigroups by solving Stieltjes renewal equations. Zbl 0770.47012
Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst R.
1993
On the stability of the cell-size distribution. II. Time-periodic development rates. Zbl 0667.92015
Diekmann, O.; Heijmans, H. J. A. M.; Thieme, H. R.
1986
Persistence and global stability for a class of discrete time structured population models. Zbl 1306.37099
Smith, Hal L.; Thieme, Horst R.
2013
An endemic model with variable re-infection rate and applications to influenza. Zbl 1020.92028
Thieme, Horst R.; Yang, Jinling
2002
Persistence and critical domain size for diffusing populations with two sexes and short reproductive season. Zbl 1369.92097
Jin, Wen; Smith, Hal L.; Thieme, Horst R.
2016
Eigenfunctionals of homogeneous order-preserving maps with applications to sexually reproducing populations. Zbl 06643381
Thieme, Horst R.
2016
Chemostats and epidemics: competition for nutrients/hosts. Zbl 1273.92039
Smith, Hal L.; Thieme, Horst R.
2013
Relatively compact orbits and compact attractors for a class of nonlinear evolution equations. Zbl 1055.34119
Thieme, Horst R.; Vrabie, Ioan I.
2003
Lack of uniqueness in transport equations with a nonlocal nonlinearity. Zbl 1012.45007
Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst R.
2000
Global stability in cyclic epidemic models with disease fatalities. Zbl 0924.92018
Thieme, Horst R.; van den Driessche, P.
1999
Perturbation theory for dual semigroups. III: Nonlinear Lipschitz continuous perturbations in the sunreflexive. Zbl 0675.47036
Clément, Ph.; Diekmann, O.; Gyllenberg, M.; Heijmans, H. J. A. M.; Thieme, H. R.
1989
An extinction/persistence threshold for sexually reproducing populations: the cone spectral radius. Zbl 1327.39012
Jin, Wen; Thieme, Horst
2016
Persistence and extinction of diffusing populations with two sexes and short reproductive season. Zbl 1305.92062
Thieme, Horst R.; Jin, Wen
2014
Stability and persistence in a model for bluetongue dynamics. Zbl 1231.34147
Gourley, Stephen A.; Thieme, Horst R.; van den Driessche, P.
2011
A sharp threshold for disease persistence in host metapopulations. Zbl 1284.92100
Dhirasakdanon, Thanate; Thieme, Horst R.; van den Driessche, Pauline
2007
An apparent paradox of horizontal and vertical disease transmission. Zbl 1140.92019
Faeth, Stanley H.; Hadeler, Karl P.; Thieme, Horst R.
2007
The “cumulative” formulation of (physiologically) structured population models. Zbl 0795.92021
Diekmann, O.; Gyllenberg, Mats; Metz, J. A. J.; Thieme, Horst
1993
A Hille-Yosida theorem for a class of weakly $${}^*$$ continuous semigroups. Zbl 0727.47025
Clément, Ph.; Dieckmann, O.; Gyllenberg, M.; Heijmans, H. J. A. M.; Thieme, H. R.
1989
Global asymptotic stability in epidemic models. Zbl 0533.92023
Thieme, Horst R.
1983
Spectral radii and Collatz-Wielandt numbers for homogeneous order-preserving maps and the monotone companion norm. Zbl 1411.47012
Thieme, Horst R.
2016
Stability and persistence in ODE models for populations with many stages. Zbl 1369.92095
Fan, Guihong; Lou, Yijun; Thieme, Horst R.; Wu, Jianhong
2015
An epidemic model with post-contact prophylaxis of distributed length. II: Stability and oscillations if treatment is fully effective. Zbl 1337.34076
Thieme, H. R.; Tridane, A.; Kuang, Y.
2008
An epidemic model with post-contact prophylaxis of distributed length I. Thresholds for disease persistence and extinction. Zbl 1140.92023
Thieme, Horst R.; Tridane, Abdessamad; Kuang, Yang
2008
Analysis of age-structured population models with an additional structure. Zbl 0748.92009
Thieme, Horst R.
1991
Perturbation theory for dual semigroups. IV: The intertwining formula and the canonical pairing. Zbl 0699.47028
Clément, Philippe; Diekmann, Odo; Gyllenberg, Mats; Heijmans, H. J. A. M.; Thieme, H. R.
1989
Asymptotic proportionality (weak ergodicity) and conditional asymptotic equality of solutions to time-heterogeneous sublinear difference and differential equations. Zbl 0652.34081
Thieme, Horst R.
1988
The asymptotic behaviour of solutions of nonlinear integral equations. Zbl 0348.45019
Thieme, Horst R.
1977
Population dynamics under selection and mutation: long-time behavior for differential equations in measure spaces. Zbl 1338.92093
Ackleh, Azmy S.; Cleveland, John; Thieme, Horst R.
2016
Persistence versus extinction for a class of discrete-time structured population models. Zbl 1347.37126
Jin, Wen; Smith, Hal L.; Thieme, Horst R.
2016
Monotone dependence of the spectral bound on the transition rates in linear compartment models. Zbl 1161.92043
Hadeler, K. P.; Thieme, H. R.
2008
Disease extinction and disease persistence in age structured epidemic models. Zbl 1042.92513
Thieme, Horst R.
2001
Balanced exponential growth for perturbed operator semigroups. Zbl 0999.47026
Thieme, Horst R.
2000
Positive perturbations of dual and integrated semigroups. Zbl 0860.47027
Thieme, Horst R.
1996
Perturbation theory for dual semigroups. V: Variation of constants formulas. Zbl 0746.47019
Diekmann, O.; Gyllenberg, M.; Thieme, H. R.
1991
Local stability in epidemic models for heterogeneous populations. Zbl 0584.92020
Thieme, Horst R.
1985
Renewal theorems for some mathematical models in epidemiology. Zbl 0565.92020
Thieme, Horst R.
1985
Do fatal infectious diseases eradicate host species? Zbl 1404.92181
Farrell, Alex P.; Collins, James P.; Greer, Amy L.; Thieme, Horst R.
2018
Times from infection to disease-induced death and their influence on final population sizes after epidemic outbreaks. Zbl 1396.92082
Farrell, Alex P.; Collins, James P.; Greer, Amy L.; Thieme, Horst R.
2018
From homogeneous eigenvalue problems to two-sex population dynamics. Zbl 06788720
Thieme, Horst R.
2017
Uniform persistence in a model for bluetongue dynamics. Zbl 1300.34185
Gourley, Stephen A.; Röst, Gergely; Thieme, Horst R.
2014
A metapopulation model with discrete size structure. Zbl 1128.92050
Martcheva, Maia; Thieme, Horst R.
2005
On the complex formation approach in modeling predator prey relations, mating, and sexual disease transmission. Zbl 0991.92023
Thieme, Horst R.; Yang, Jinling
2000
Perturbing evolutionary systems by step responses and cumulative outputs. Zbl 0834.47043
Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst R.
1995
Some theoretical and numerical aspects of modelling dispersion in the development of ectotherms. Zbl 0661.92022
Schuhmacher, K.; Thieme, H.
1988
Spread of viral infection of immobilized bacteria. Zbl 1267.92050
Jones, Don A.; Smith, Hal L.; Thieme, Horst R.
2013
Numerical simulations of the spread of rabies in two-dimensional space. Zbl 1404.65132
Alanazi, Khalaf M.; Jackiewicz, Zdzislaw; Thieme, Horst R.
2019
Do fatal infectious diseases eradicate host species? Zbl 1404.92181
Farrell, Alex P.; Collins, James P.; Greer, Amy L.; Thieme, Horst R.
2018
Times from infection to disease-induced death and their influence on final population sizes after epidemic outbreaks. Zbl 1396.92082
Farrell, Alex P.; Collins, James P.; Greer, Amy L.; Thieme, Horst R.
2018
Correction to: “Measures under the flat norm as ordered normed vector space”. Zbl 1390.28005
Gwiazda, Piotr; Marciniak-Czochra, Anna; Thieme, Horst R.
2018
Measures under the flat norm as ordered normed vector space. Zbl 1390.28004
Gwiazda, Piotr; Marciniak-Czochra, Anna; Thieme, Horst R.
2018
From homogeneous eigenvalue problems to two-sex population dynamics. Zbl 06788720
Thieme, Horst R.
2017
Competition in the chemostat with time-dependent differential removal rates. Zbl 1372.92061
Fan, Guihong; Smith, Hal L.; Thieme, Horst R.
2017
Eigenvectors of homogeneous order-bounded order-preserving maps. Zbl 06707638
Thieme, Horst R.
2017
Persistence and critical domain size for diffusing populations with two sexes and short reproductive season. Zbl 1369.92097
Jin, Wen; Smith, Hal L.; Thieme, Horst R.
2016
Eigenfunctionals of homogeneous order-preserving maps with applications to sexually reproducing populations. Zbl 06643381
Thieme, Horst R.
2016
An extinction/persistence threshold for sexually reproducing populations: the cone spectral radius. Zbl 1327.39012
Jin, Wen; Thieme, Horst
2016
Spectral radii and Collatz-Wielandt numbers for homogeneous order-preserving maps and the monotone companion norm. Zbl 1411.47012
Thieme, Horst R.
2016
Population dynamics under selection and mutation: long-time behavior for differential equations in measure spaces. Zbl 1338.92093
Ackleh, Azmy S.; Cleveland, John; Thieme, Horst R.
2016
Persistence versus extinction for a class of discrete-time structured population models. Zbl 1347.37126
Jin, Wen; Smith, Hal L.; Thieme, Horst R.
2016
Spread of phage infection of bacteria in a petri dish. Zbl 1336.92082
Jones, Don A.; Smith, Hal L.; Thieme, Horst R.
2016
Delay differential systems for tick population dynamics. Zbl 1355.92087
Fan, Guihong; Thieme, Horst R.; Zhu, Huaiping
2015
Stability and persistence in ODE models for populations with many stages. Zbl 1369.92095
Fan, Guihong; Lou, Yijun; Thieme, Horst R.; Wu, Jianhong
2015
Persistence and extinction of diffusing populations with two sexes and short reproductive season. Zbl 1305.92062
Thieme, Horst R.; Jin, Wen
2014
Uniform persistence in a model for bluetongue dynamics. Zbl 1300.34185
Gourley, Stephen A.; Röst, Gergely; Thieme, Horst R.
2014
Persistence and global stability for a class of discrete time structured population models. Zbl 1306.37099
Smith, Hal L.; Thieme, Horst R.
2013
Chemostats and epidemics: competition for nutrients/hosts. Zbl 1273.92039
Smith, Hal L.; Thieme, Horst R.
2013
Spread of viral infection of immobilized bacteria. Zbl 1267.92050
Jones, Don A.; Smith, Hal L.; Thieme, Horst R.
2013
Persistence of bacteria and phages in a chemostat. Zbl 1303.92123
Smith, Hal L.; Thieme, Horst R.
2012
On spread of phage infection of bacteria in a Petri dish. Zbl 1243.92041
Jones, Don A.; Smith, Hal L.; Thieme, Horst R.; Röst, Gergely
2012
Dynamical systems and population persistence. Zbl 1214.37002
Smith, Hal L.; Thieme, Horst R.
2011
Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators. Zbl 1215.37052
Thieme, Horst R.
2011
Stability and persistence in a model for bluetongue dynamics. Zbl 1231.34147
Gourley, Stephen A.; Thieme, Horst R.; van den Driessche, P.
2011
Stability of the endemic coexistence equilibrium for one host and two parasites. Zbl 1205.92063
Dhirasakdanon, T.; Thieme, H. R.
2010
Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity. Zbl 1191.47089
Thieme, Horst R.
2009
Species decline and extinction: synergy of infectious disease and Allee effect? Zbl 1342.92206
Thieme, Horst R.; Dhirasakdanon, Thanate; Han, Zhun; Trevino, Roy
2009
Distributed susceptibility: a challenge to persistence theory in infectious disease models. Zbl 1179.92054
Thieme, Horst R.
2009
Relatively bounded extensions of generator perturbations. Zbl 1181.47048
Thieme, Horst R.; Voigt, Jürgen
2009
Differentiability of convolutions, integrated semigroups of bounded semi-variation, and the inhomogeneous Cauchy problem. Zbl 1157.45007
Thieme, Horst R.
2008
An epidemic model with post-contact prophylaxis of distributed length. II: Stability and oscillations if treatment is fully effective. Zbl 1337.34076
Thieme, H. R.; Tridane, A.; Kuang, Y.
2008
An epidemic model with post-contact prophylaxis of distributed length I. Thresholds for disease persistence and extinction. Zbl 1140.92023
Thieme, Horst R.; Tridane, Abdessamad; Kuang, Yang
2008
Monotone dependence of the spectral bound on the transition rates in linear compartment models. Zbl 1161.92043
Hadeler, K. P.; Thieme, H. R.
2008
Markov transition functions and semigroups of measures. Zbl 1146.47030
Lant, Timothy; Thieme, Horst R.
2007
A sharp threshold for disease persistence in host metapopulations. Zbl 1284.92100
Dhirasakdanon, Thanate; Thieme, Horst R.; van den Driessche, Pauline
2007
An apparent paradox of horizontal and vertical disease transmission. Zbl 1140.92019
Faeth, Stanley H.; Hadeler, Karl P.; Thieme, Horst R.
2007
Multiparametric bifurcation analysis of a basic two-stage population model. Zbl 1106.34030
Baer, S. M.; Kooi, B. W.; Kuznetsov, Yu. A.; Thieme, H. R.
2006
Stochastic semigroups: their construction by perturbation and approximation. Zbl 1113.47029
Thieme, H. R.; Voigt, J.
2006
Perturbing evolutionary systems on dual spaces by cumulative outputs. Zbl 1211.47014
Gyllenberg, Mats; Lant, Timothy; Thieme, Horst R.
2006
Kolmogorov’s differential equations and positive semigroups on first moment sequence spaces. Zbl 1113.92069
Martcheva, Maia; Thieme, Horst R.; Dhirasakdanon, Thanate
2006
Rate distributions and survival of the fittest: a formulation on the space of measures. Zbl 1078.92055
Ackleh, Azmy S.; Fitzpatrick, Ben G.; Thieme, Horst R.
2005
A metapopulation model with discrete size structure. Zbl 1128.92050
Martcheva, Maia; Thieme, Horst R.
2005
Eventual compactness for semiflows generated by nonlinear age-structured models. Zbl 1083.47061
Magal, P.; Thieme, H. R.
2004
Semilinear perturbations of Hille–Yosida operators. Zbl 1073.47063
Thieme, Horst R.; Vosseler, Hauke
2004
Mathematics in population biology. Zbl 1054.92042
Thieme, Horst R.
2003
Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction–diffusion models. Zbl 1045.45009
Thieme, Horst R.; Zhao, Xiao-Qiang
2003
Progression age enhanced backward bifurcation in an epidemic model with super-infection. Zbl 1097.92046
Martcheva, Maia; Thieme, Horst R.
2003
Relatively compact orbits and compact attractors for a class of nonlinear evolution equations. Zbl 1055.34119
Thieme, Horst R.; Vrabie, Ioan I.
2003
Competitive dynamics in a model for onchocerciasis with cross-immunity. Zbl 1078.92038
Mopecha, Jimmy P.; Thieme, Horst R.
2003
An endemic model with variable re-infection rate and applications to influenza. Zbl 1020.92028
Thieme, Horst R.; Yang, Jinling
2002
The transition through stages with arbitrary length distributions, and applications in epidemics. Zbl 1056.92038
Thieme, Horst R.
2002
Nonlinear mating models for populations with discrete generations. Zbl 1024.92018
Castillo-Chavez, Carlos; Yakubu, Abdul-Aziz; Thieme, Horst; Martcheva, Maia
2002
A Stieltjes type convolution for integrated semigroups of bounded strong variation and $$L_p$$-solutions to the abstract Cauchy problem. Zbl 1041.47029
Thieme, Horst R.; Vosseler, Hauke
2002
A non-local delayed and diffusive predator-prey model. Zbl 1113.92319
Thieme, Horst R.; Zhao, Xiao-Qiang
2001
Stable coexistence and bi-stability for competitive systems on ordered Banach spaces. Zbl 1064.47075
Smith, H. L.; Thieme, H. R.
2001
Disease extinction and disease persistence in age structured epidemic models. Zbl 1042.92513
Thieme, Horst R.
2001
Uniform persistence and permanence for non-autonomous semiflows in population biology. Zbl 0970.37061
Thieme, Horst R.
2000
Endemic models with arbitrarily distributed periods of infection. I: Fundamental properties of the model. Zbl 0991.92028
Feng, Zhilan; Thieme, Horst R.
2000
Endemic models with arbitrarily distributed periods of infection. II: Fast disease dynamics and permanent recovery. Zbl 1016.92035
Feng, Zhilan; Thieme, Horst R.
2000
Lack of uniqueness in transport equations with a nonlocal nonlinearity. Zbl 1012.45007
Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst R.
2000
Balanced exponential growth for perturbed operator semigroups. Zbl 0999.47026
Thieme, Horst R.
2000
On the complex formation approach in modeling predator prey relations, mating, and sexual disease transmission. Zbl 0991.92023
Thieme, Horst R.; Yang, Jinling
2000
Uniform weak implies uniform strong persistence for nonautonomous semiflows. Zbl 0918.34053
Thieme, Horst R.
1999
Global stability in cyclic epidemic models with disease fatalities. Zbl 0924.92018
Thieme, Horst R.; van den Driessche, P.
1999
On the formulation and analysis of general deterministic structured population models. I: Linear theory. Zbl 0909.92023
Diekmann, Odo; Gyllenberg, Mats; Metz, J. A. J.; Thieme, Horst R.
1998
Positive perturbation of operator semigroups: Growth bounds, essential compactness, and asynchronous exponential growth. Zbl 0988.47024
Thieme, Horst R.
1998
Balanced exponential growth of operator semigroups. Zbl 0943.47032
Thieme, Horst R.
1998
Remarks on resolvent positive operators and their perturbation. Zbl 0962.47017
Thieme, Horst R.
1998
Quasi-compact semigroups via bounded perturbation. Zbl 0945.47033
Thieme, Horst R.
1997
Positive perturbations of dual and integrated semigroups. Zbl 0860.47027
Thieme, Horst R.
1996
Nonlinear perturbations of a class of integrated semigroups. Zbl 0872.47032
Matsumoto, Toshitaka; Oharu, Shinnosuke; Thieme, Horst R.
1996
On commutative sums of generators. Zbl 0890.47027
Thieme, Horst R.
1996
Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Zbl 0829.34037
Mischaikow, Konstantin; Smith, Hal; Thieme, Horst R.
1995
Recurrent outbreaks of childhood diseases revisited: The impact of isolation. Zbl 0833.92017
Feng, Zhilan; Thieme, Horst R.
1995
Perturbing evolutionary systems by step responses and cumulative outputs. Zbl 0834.47043
Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst R.
1995
Asymptotically autonomous differential equations in the plane. Zbl 0811.34036
Thieme, Horst R.
1994
Asymptotically autonomous differential equations in the plane. II: Stricter Poincaré/Bendixson type results. Zbl 0811.34037
Thieme, Horst R.
1994
Persistence under relaxed point-dissipativity (with application to an endemic model). Zbl 0774.34030
Thieme, Horst R.
1993
How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS? Zbl 0811.92021
Thieme, Horst R.; Castillo-Chavez, Carlos
1993
Dynamics of an age structured epidemic model. Zbl 0943.92502
Busenberg, Stavros; Iannelli, Mimmo; Thieme, Horst
1993
Perturbing semigroups by solving Stieltjes renewal equations. Zbl 0770.47012
Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst R.
1993
The “cumulative” formulation of (physiologically) structured population models. Zbl 0795.92021
Diekmann, O.; Gyllenberg, Mats; Metz, J. A. J.; Thieme, Horst
1993
Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations. Zbl 0761.34039
Thieme, Horst R.
1992
Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations. Zbl 0782.92018
Thieme, Horst R.
1992
Global behavior of an age-structured epidemic model. Zbl 0741.92015
Busenberg, Stavros N.; Iannelli, Mimmo; Thieme, Horst R.
1991
Strongly order preserving semiflows generated by functional differential equations. Zbl 0735.34065
Smith, Hal L.; Thieme, Horst R.
1991
Convergence for strongly order-preserving semiflows. Zbl 0739.34040
Smith, Hal L.; Thieme, Horst R.
1991
Stability change of the endemic equilibrium in age-structured models for the spread of S-I-R type infectious diseases. Zbl 0748.92013
Thieme, Horst R.
1991
Demographic change and persistence of HIV/AIDS in a heterogeneous population. Zbl 0739.92014
Busenberg, Stavros; Cooke, Kenneth; Thieme, Horst
1991
Analysis of age-structured population models with an additional structure. Zbl 0748.92009
Thieme, Horst R.
1991
Perturbation theory for dual semigroups. V: Variation of constants formulas. Zbl 0746.47019
Diekmann, O.; Gyllenberg, M.; Thieme, H. R.
1991
Semigroups and renewal equations on dual Banach spaces with applications to population dynamics. Zbl 0799.47022
Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst R.
1991
Semiflows generated by Lipschitz perturbations of non-densely defined operators. Zbl 0734.34059
Thieme, Horst R.
1990
“Integrated semigroups” and integrated solutions to abstract Cauchy problems. Zbl 0738.47037
Thieme, Horst R.
1990
Quasi convergence and stability for strongly order-preserving semiflows. Zbl 0704.34054
Smith, Hal L.; Thieme, Horst R.
1990
Monotone semiflows in scalar non-quasi-monotone functional differential equations. Zbl 0719.34123
Smith, Hal L.; Thieme, Horst R.
1990
A competitive exclusion principle for pathogen virulence. Zbl 0715.92027
Bremermann, H. J.; Thieme, H. R.
1989
...and 26 more Documents
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#### Cited by 2,785 Authors

 66 Zhao, Xiao-Qiang 59 Thieme, Horst R. 49 Ruan, Shigui 43 Li, Xuezhi 40 Martcheva, Maia 39 Zou, Xingfu 34 Smith, Hal Leslie 34 Wang, Jinliang 33 Magal, Pierre 32 Teng, Zhi-dong 32 Wu, Jianhong 31 Wang, Wendi 29 Gyllenberg, Mats 29 Qiu, Zhipeng 28 Kuniya, Toshikazu 27 Wang, Feng-Bin 26 Feng, Zhilan 26 Webb, Glenn Francis 26 Yang, Junyuan 25 Cai, Liming 25 Diekmann, Odo 24 Jin, Zhen 23 Li, Wan-Tong 22 Liu, Shengqiang 21 Chen, Yuming 20 Kang, Yun 20 Wu, Shiliang 19 Jang, Sophia R.-J. 19 Zhang, Tailei 18 Liu, Xianning 18 Liz, Eduardo 18 Takeuchi, Yasuhiro 18 Yuan, Rong 17 Ducrot, Arnaud 17 Gumel, Abba B. 17 Inaba, Hisashi 17 Kuang, Yang 17 Lin, Guo 17 Liu, Chao 17 Liu, Zhihua 17 Rong, Libin 17 Weng, Peixuan 16 Ezzinbi, Khalil 16 Ma, Wanbiao 16 Metz, Johan A. Jacob 15 Ackleh, Azmy S. 15 Bacaër, Nicolas 15 Castillo-Chavez, Carlos 15 Chattopadhyay, Joydev 15 Lou, Yijun 15 Wei, Junjie 14 Hsu, Cheng-Hsiung 14 Hsu, Szebi 14 Shi, Junping 13 Cui, Jingan 13 Ghosh, Mini 13 Liu, Junli 13 Song, Xinyu 13 Trofimchuk, Sergei I. 12 Bai, Zhenguo 12 Bhunu, Claver Pedzisai 12 Calsina, Àngel 12 Jiang, Jifa 12 Mushayabasa, Steady 12 Wang, Wei 12 Wang, Xia 12 Wang, Zhi Cheng 12 Xu, Rui 12 Zhang, Qingling 11 Gwiazda, Piotr 11 Li, Bingtuan 11 Li, Michael Yi 11 Rass, Linda 11 Röst, Gergely 11 Zhou, Yicang 10 Garira, Winston S. 10 Liang, Xing 10 Nakaoka, Shinji 10 Sun, Guiquan 10 van den Driessche, Pauline 10 Wang, Hao 10 Wang, Jin 10 Wu, YiXiang 10 Yi, Taishan 10 Zhang, Long 9 Adimy, Mostafa 9 Bowong, Samuel 9 d’Onofrio, Alberto 9 Gourley, Stephen A. 9 Heijmans, Henk J. A. M. 9 Huo, Hai-Feng 9 Imran, Mudassar 9 Lewis, Mark Alun 9 Liu, Lili 9 Mukandavire, Zindoga 9 Obaya, Rafael 9 Pugliese, Andrea 9 Radcliffe, John 9 Samanta, Guru Prasad 9 Wang, Xueying ...and 2,685 more Authors
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#### Cited in 227 Serials

 187 Journal of Mathematical Biology 154 Mathematical Biosciences 134 Journal of Mathematical Analysis and Applications 134 Journal of Differential Equations 106 Applied Mathematics and Computation 104 Nonlinear Analysis. Real World Applications 103 Discrete and Continuous Dynamical Systems. Series B 100 Bulletin of Mathematical Biology 85 Journal of Biological Dynamics 64 Journal of Theoretical Biology 63 International Journal of Biomathematics 53 Journal of Dynamics and Differential Equations 49 Mathematical Biosciences and Engineering 40 Mathematical and Computer Modelling 36 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 36 Applied Mathematical Modelling 35 Theoretical Population Biology 34 Journal of Biological Systems 32 Computers & Mathematics with Applications 29 Chaos, Solitons and Fractals 29 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 28 Journal of Difference Equations and Applications 27 Abstract and Applied Analysis 26 SIAM Journal on Applied Mathematics 26 Advances in Difference Equations 25 Mathematical Methods in the Applied Sciences 25 Communications in Nonlinear Science and Numerical Simulation 22 Journal of Computational and Applied Mathematics 22 Communications on Pure and Applied Analysis 20 Applicable Analysis 20 Discrete Dynamics in Nature and Society 19 Applied Mathematics Letters 19 Mathematical Modelling of Natural Phenomena 18 Journal of Applied Mathematics and Computing 17 Journal of the Franklin Institute 15 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 15 Journal of Applied Analysis and Computation 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 14 Journal of Nonlinear Science 13 Rocky Mountain Journal of Mathematics 13 Transactions of the American Mathematical Society 13 Discrete and Continuous Dynamical Systems 12 Proceedings of the American Mathematical Society 12 Semigroup Forum 12 Acta Applicandae Mathematicae 12 Complexity 11 Journal of Evolution Equations 10 Mathematical Population Studies 10 Nonlinear Dynamics 9 Physica D 9 Acta Mathematicae Applicatae Sinica. English Series 9 European Journal of Applied Mathematics 9 Journal of Applied Mathematics 8 SIAM Journal on Mathematical Analysis 8 Computational and Applied Mathematics 8 Mathematical Problems in Engineering 8 Differential Equations and Dynamical Systems 7 Nonlinearity 7 Mathematics and Computers in Simulation 6 Automatica 6 Journal of Integral Equations and Applications 6 Japan Journal of Industrial and Applied Mathematics 6 International Journal of Computer Mathematics 6 Positivity 6 SIAM Journal on Applied Dynamical Systems 6 Computational & Mathematical Methods in Medicine 6 Discrete and Continuous Dynamical Systems. Series S 5 Journal of Statistical Physics 5 Ricerche di Matematica 5 Systems & Control Letters 5 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 5 Qualitative Theory of Dynamical Systems 5 The ANZIAM Journal 5 Science China. Mathematics 5 Afrika Matematika 4 Physica A 4 Mathematische Annalen 4 Applied Numerical Mathematics 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Calculus of Variations and Partial Differential Equations 4 Chaos 4 International Journal of Nonlinear Sciences and Numerical Simulation 4 Dynamical Systems 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Mediterranean Journal of Mathematics 4 Journal of Nonlinear Science and Applications 4 Mathematics 4 Nonlinear Analysis. Theory, Methods & Applications 4 International Journal of Applied and Computational Mathematics 4 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 3 Archive for Rational Mechanics and Analysis 3 Indian Journal of Pure & Applied Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Czechoslovak Mathematical Journal 3 Mathematische Zeitschrift 3 Monatshefte für Mathematik 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Numerical Methods for Partial Differential Equations 3 Linear Algebra and its Applications 3 Stochastic Processes and their Applications ...and 127 more Serials
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#### Cited in 42 Fields

 2,056 Biology and other natural sciences (92-XX) 1,012 Ordinary differential equations (34-XX) 743 Partial differential equations (35-XX) 472 Dynamical systems and ergodic theory (37-XX) 221 Operator theory (47-XX) 169 Integral equations (45-XX) 157 Numerical analysis (65-XX) 108 Probability theory and stochastic processes (60-XX) 97 Systems theory; control (93-XX) 89 Difference and functional equations (39-XX) 68 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 54 Calculus of variations and optimal control; optimization (49-XX) 23 Functional analysis (46-XX) 15 Combinatorics (05-XX) 15 Computer science (68-XX) 14 Statistics (62-XX) 11 Statistical mechanics, structure of matter (82-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 9 Global analysis, analysis on manifolds (58-XX) 9 Operations research, mathematical programming (90-XX) 5 Measure and integration (28-XX) 5 Mechanics of particles and systems (70-XX) 4 Integral transforms, operational calculus (44-XX) 4 General topology (54-XX) 4 Mechanics of deformable solids (74-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Information and communication theory, circuits (94-XX) 2 Abstract harmonic analysis (43-XX) 2 Quantum theory (81-XX) 2 Astronomy and astrophysics (85-XX) 2 Mathematics education (97-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Fluid mechanics (76-XX) 1