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Global dynamics of delay‐distributed HIV infection models with differential drug efficacy in cocirculating target cells
Author(s) -
Elaiw A. M.,
Almuallem N. A.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3453
Subject(s) - mathematics , lyapunov function , basic reproduction number , stability theory , bilinear interpolation , human immunodeficiency virus (hiv) , stability (learning theory) , exponential stability , delay differential equation , differential equation , mathematical analysis , population , computer science , statistics , nonlinear system , biology , virology , physics , demography , quantum mechanics , machine learning , sociology
In this paper, we investigate the dynamical behaviors of three human immunodeficiency virus infection models with two types of cocirculating target cells and distributed intracellular delay. The models take into account both short‐lived infected cells and long‐lived chronically infected cells. In the two types of target cells, the drug efficacy is assumed to be different. The incidence rate of infection is given by bilinear and saturation functional responses in the first and second models, respectively, while it is given by a general function in the third model. Lyapunov functionals are constructed and LaSalle invariance principle is applied to prove the global asymptotic stability of all equilibria of the models. We have derived the basic reproduction number R 0 for the three models. For the first two models, we have proven that the disease‐free equilibrium is globally asymptotically stable (GAS) when R 0 ≤1, and the endemic equilibrium is GAS when R 0 >1. For the third model, we have established a set of sufficient conditions for global stability of both equilibria of the model. We have checked our theoretical results with numerical simulations. Copyright © 2015 John Wiley & Sons, Ltd.