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Solving a class of biological HIV infection model of latently infected cells using heuristic approach. (English) Zbl 1471.92309

Summary: The intension of the recent study is to solve a class of biological nonlinear HIV infection model of latently infected \(\text{CD}4^+\)T cells using feed-forward artificial neural networks, optimized with global search method, i.e. particle swarm optimization (PSO) and quick local search method, i.e. interior-point algorithms (IPA). An unsupervised error function is made based on the differential equations and initial conditions of the HIV infection model represented with latently infected \(\text{CD}4^+\)T cells. For the correctness and reliability of the present scheme, comparison is made of the present results with the Adams numerical results. Moreover, statistical measures based on mean absolute deviation, Theil’s inequality coefficient as well as root mean square error demonstrates the effectiveness, applicability and convergence of the designed scheme.

MSC:

92D30 Epidemiology
68T07 Artificial neural networks and deep learning
90C59 Approximation methods and heuristics in mathematical programming
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[1] G. Adomian, Solving frontier problems modelled by nonlinear partial differential equations, Computers & Mathematics with Applications, 22, 91-94 (1991) · Zbl 0767.35016
[2] I. Ahmad, et al., Novel applications of intelligent computing paradigms for the analysis of nonlinear reactive transport model of the fluid in soft tissues and microvessels, Neural Computing and Applications, 31 (2019), 9041-9059.
[3] I. Ahmad, et al., Anticipated backward doubly stochastic differential equations with nonLiphschitz coefficients, Applied Mathematics and Nonlinear Sciences, 4 (2019), 9-20. · Zbl 1524.60109
[4] S. Akbar, et al., Novel application of FO-DPSO for 2-D parameter estimation of electromagnetic plane waves, Neural Computing and Applications, 31 (2019), 3681-3690.
[5] K. S. Al-Ghafri; H. Rezazadeh, Solitons and other solutions of (3+ 1)-dimensional space-time fractional modified KdV-Zakharov-Kuznetsov equation, Applied Mathematics and Nonlinear Sciences, 4, 289-304 (2019) · Zbl 1506.35258
[6] N. Ali and G. Zaman, Asymptotic behavior of HIV-1 epidemic model with infinite distributed intracellular delays, Springer Plus, 5 (2016), 324.
[7] N. Ali, G. Zaman and O. Algahtani, Stability analysis of HIV-1 model with multiple delays, Advances in Difference Equations, 2016 (2016), 88. · Zbl 1344.92148
[8] N. Ali; S. Ahmad; S. Aziz; G. Zaman, The Adomian decomposition method for solving HIV infection model of latently infected cells, Matrix Science Mathematic, 3, 5-8 (2019)
[9] J. Bleyer, Advances in the simulation of viscoplastic fluid flows using interior-point methods, Computer Methods in Applied Mechanics and Engineering, 330, 368-394 (2018) · Zbl 1439.76006
[10] D. W. Brzezinski, Review of numerical methods for NumILPT with computational accuracy assessment for fractional calculus, Applied Mathematics and Nonlinear Sciences, 3, 487-502 (2018) · Zbl 1515.65320
[11] D. W. Brzezinski, Comparison of fractional order derivatives computational accuracy-right hand vs left hand definition, Applied Mathematics and Nonlinear Sciences, 2, 237-248 (2017) · Zbl 1379.65015
[12] S. Effati; M. Pakdaman, Artificial neural network approach for solving fuzzy differential equations, Information Sciences, 180, 1434-1457 (2010) · Zbl 1185.65114
[13] A. P. Engelbrecht, Computational Intelligence: An Introduction, John Wiley & Sons, 2007.
[14] A. A. Esmin; R. A. Coelho; S. Matwin, A review on particle swarm optimization algorithm and its variants to clustering high-dimensional data, Artificial Intelligence Review, 44, 23-45 (2015)
[15] M. F. Fateh, et al., Differential evolution based computation intelligence solver for elliptic partial differential equations, Frontiers of Information Technology & Electronic Engineering, 20 (2019), 1445-1456.
[16] M. Ghoreishi; A. M. Ismail; A. K. Alomari, Application of the homotopy analysis method for solving a model for HIV infection of CD4+ T-cells, Mathematical and Computer Modelling, 54, 3007-3015 (2011) · Zbl 1235.65095
[17] K. Hattaf; N. Yousfi, Global properties of a discrete viral infection model with general incidence rate, Mathematical Methods in the Applied Sciences, 39, 998-1004 (2016) · Zbl 1336.92081
[18] K. Hattaf; N. Yousfi, A numerical method for a delayed viral infection model with general incidence rate, Journal of King Saud University-Science, 28, 368-374 (2016)
[19] K. Hattaf and N. Yousfi, Modeling the adaptive immunity and both modes of transmission in HIV infection, Computation, 6 (2018), 37. · Zbl 1487.92042
[20] K. Hattaf, Spatiotemporal dynamics of a generalized viral infection model with distributed delays and CTL immune response, Computation, 7 (2019), 21.
[21] W. He; Y. Chen; Z. Yin, Adaptive neural network control of an uncertain robot with full-state constraints, IEEE transactions on cybernetics, 46, 620-629 (2015)
[22] A. Khare; S. Rangnekar, A review of particle swarm optimization and its applications in solar photovoltaic system, Applied Soft Computing, 13, 2997-3006 (2013)
[23] D. Mangoni; A. Tasora; A.; R. Garziera, A primal-dual predictor-corrector interior point method for non-smooth contact dynamics, Computer Methods in Applied Mechanics and Engineering, 330, 351-367 (2018) · Zbl 1439.74226
[24] A. Mehmood, et al., Integrated intelligent computing paradigm for the dynamics of micropolar fluid flow with heat transfer in a permeable walled channel, Applied Soft Computing, 79 (2019), 139-162.
[25] A. Mehmood, et al., Backtracking search heuristics for identification of electrical muscle stimulation models using Hammerstein structure, Applied Soft Computing, 84 (2019), 105705.
[26] S. Momani, Z. S. Abo-Hammour and O. M. Alsmadi, Solution of inverse kinematics problem using genetic algorithms, Applied Mathematics & Information Sciences, 10 (2016), 225.
[27] F. Pelletier; C. Masson; A. Tahan, Wind turbine power curve modelling using artificial neural network, Renewable Energy, 89, 207-214 (2016)
[28] A. S. Perelson, Modeling the interaction of the immune system with HIV, Mathematical and Statistical Approaches to AIDS Epidemiology, Springer, Berlin, Heidelberg, 1989,350-370. · Zbl 0683.92001
[29] A. S. Perelson; D. E. Kirschner; R. De Boer, Dynamics of HIV infection of CD4+ T cells. Mathematical biosciences, Mathematical Biosciences, 114, 81-125 (1993) · Zbl 0796.92016
[30] M. Prague, Use of dynamical models for treatment optimization in HIV infected patients: A sequential Bayesian analysis approach, Journal de la Societe Francaise de Statistique, 157 (2016), 20. · Zbl 1358.62103
[31] M. A. Z. Raja; F. H. Shah; M. Tariq; I. Ahmad, Design of artificial neural network models optimized with sequential quadratic programming to study the dynamics of nonlinear Troesch’s problem arising in plasma physics, Neural Computing and Applications, 29, 83-109 (2018)
[32] M. A. Z. Raja; J. A. Khan; T. Haroon, Stochastic numerical treatment for thin film flow of third grade fluid using unsupervised neural networks, Journal of the Taiwan Institute of Chemical Engineers, 48, 26-39 (2015)
[33] M. A. Z. Raja; U. Farooq; N. I. Chaudhary; A. M. Wazwaz; M. A., Stochastic numerical solver for nanofluidic problems containing multi-walled carbon nanotubes, Applied Soft Computing, 38, 561-586 (2016)
[34] M. A. Z. Raja; J. Mehmood; Z. Sabir; A. K. Nasab; M. A. Manzar, Numerical solution of doubly singular nonlinear systems using neural networks-based integrated intelligent computing, Neural Computing and Applications, 31, 793-812 (2019)
[35] M. A. Z. Raja, M. Umar, Z. Sabir, J. A. Khan and D. Baleanu, A new stochastic computing paradigm for the dynamics of nonlinear singular heat conduction model of the human head, The European Physical Journal Plus, 133 (2018), 364.
[36] M. A. Z. Raja, Solution of the one-dimensional Bratu equation arising in the fuel ignition model using ANN optimised with PSO and SQP, Connection Science, 26, 195-214 (2014)
[37] M. A. Z. Raja; M. S. Aslam; N. I. Chaudhary; M. Nawaz; S. M. Shah, Design of hybrid nature-inspired heuristics with application to active noise control systems, Neural Computing and Applications, 31, 2563-2591 (2019)
[38] M. A. Z. Raja; U. Ahmed; A. Zameer; A. K. Kiani; N. I. Chaudhary, Bio-inspired heuristics hybrid with sequential quadratic programming and interior-point methods for reliable treatment of economic load dispatch problem, Neural Computing and Applications, 31, 447-475 (2019)
[39] M. A. Z. Raja; M. S. Aslam; N. I. Chaudhary; W. U. Khan, Bio-inspired heuristics hybrid with interior-point method for active noise control systems without identification of secondary path, Frontiers of Information Technology & Electronic Engineering, 19, 246-259 (2018)
[40] E.S. Rosenberg, et al., Immune control of HIV-1 after early treatment of acute infection, Nature, 407 (2000), 523.
[41] Z. Sabir; M. A. Manzar; M. A. Z. Raja; M. Sheraz; A. M. Wazwaz, Neuro-heuristics for nonlinear singular Thomas-Fermi systems, Applied Soft Computing, 65, 152-169 (2018)
[42] Z. Sadegh; N. Miehran, A nonstandard finite difference scheme for solving fractional-order model of HIV-1 infection of CD4+t-cells, Iranian Journal of Mathematical Chemistry, 6, 169-184 (2015) · Zbl 1367.92069
[43] J. C. Schaff, F. Gao, Y. Li, I. L. Novak and B. M. Slepchenko, Numerical approach to spatial deterministic-stochastic models arising in cell biology, PLoS Computational Biology, 12 (2016), 1005236.
[44] Y. Shi and R. C. Eberhart, Empirical study of particle swarm optimization, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99, (Cat. No. 99TH8406), 3 (1999), 1945-1950).
[45] C. Soize, Stochastic models of uncertainties in computational structural dynamics and structural acoustics, Nondeterministic Mechanics, Springer, Vienna, 2012, 61-113. · Zbl 1279.74043
[46] V. K. Srivastava; M. K. Awasthi; S. Kumar, Numerical approximation for HIV infection of CD4+ T cells mathematical model, Ain Shams Engineering Journal, 5, 625-629 (2014) · Zbl 1297.01034
[47] M. Stefanova, S. Yakunin, M. Petukhova, S. Lupuleac and M. Kokkolaras, An interior-point method-based solver for simulation of aircraft parts riveting, Engineering Optimization, 50 (2018), pp.781-796. · Zbl 07636629
[48] M. Umar; Z. Sabir; M. A. Z. Raja, Intelligent computing for numerical treatment of nonlinear prey-predator models, Applied Soft Computing, 80, 506-524 (2019)
[49] S. G. Venkatesh; S. R. Balachandar; S. K. Ayyaswamy; K. Balasubramanian, A new approach for solving a model for HIV infection of CD4+ t-cells arising in mathematical chemistry using wavelets, Journal of Mathematical Chemistry, 54, 1072-1082 (2016) · Zbl 1364.92026
[50] L. Wang; M. Y. Li, Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells, Mathematical Biosciences, 200, 44-57 (2006) · Zbl 1086.92035
[51] N. Yadav; A. Yadav; M. Kumar; J. H. Kim, An efficient algorithm based on artificial neural networks and particle swarm optimization for solution of nonlinear Troesch’s problem, Neural Computing and Applications, 28, 171-178 (2017)
[52] A. Yokus; S. Gulbahar, Numerical solutions with linearization techniques of the fractional Harry Dym equation, Applied Mathematics and Nonlinear Sciences, 4, 35-42 (2019) · Zbl 1506.65133
[53] A. Yokus, Comparison of Caputo and conformable derivatives for time-fractional Korteweg-de Vries equation via the finite difference method, International Journal of Modern Physics B, 32 (2018), 1850365. · Zbl 1423.35421
[54] A. Yokus, Numerical solution for space and time fractional order Burger type equation, Alexandria Engineering Journal, 57, 2085-2091 (2018) · Zbl 1404.83150
[55] I. K. Youssef; M. H. El Dewaik, Solving Poisson’s Equations with fractional order using Haarwavelet, Applied Mathematics and Nonlinear Sciences, 2, 271-284 (2017)
[56] S. Yuzbasi, A numerical approach to solve the model for HIV infection of CD4+T cells, Applied Mathematical Modelling, 36, 5876-5890 (2012) · Zbl 1349.92098
[57] A. Zameer; M. Majeed; S. M. Mirza; M. A. Z. Raja; A. Khan; N. M. Mirza, Bio-inspired heuristics for layer thickness optimization in multilayer piezoelectric transducer for broadband structures, Soft Computing, 23, 3449-3463 (2019)
[58] A. Zameer, et al., Fractional-order particle swarm based multi-objective PWR core loading pattern optimization, Annals of Nuclear Energy, 135 (2020), 106982.
[59] A. Zameer, et al., Intelligent and robust prediction of short term wind power using genetic programming based ensemble of neural networks, Energy Conversion and Management, 134 (2017), 361-372.
[60] Z. Zhang; T. A. El-Moselhy; I. M. Elfadel; L. Daniel, Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 32, 1533-1545 (2013)
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