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Global properties of a class of HIV infection models with Beddington–DeAngelis functional response
Author(s) -
Elaiw A. M.,
Azoz S. A.
Publication year - 2012
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.2596
Subject(s) - mathematics , stability theory , steady state (chemistry) , human immunodeficiency virus (hiv) , stability (learning theory) , lyapunov function , exponential stability , class (philosophy) , basic reproduction number , virology , biology , population , computer science , physics , demography , artificial intelligence , chemistry , sociology , quantum mechanics , nonlinear system , machine learning
In this paper, the global properties of a class of human immunodeficiency virus (HIV) models with Beddington–DeAngelis functional response are investigated. Lyapunov functions are constructed to establish the global asymptotic stability of the uninfected and infected steady states of three HIV infection models. The first model considers the interaction process of the HIV and the CD4 + T cells and takes into account the latently and actively infected cells. The second model describes two co‐circulation populations of target cells, representing CD4 + T cells and macrophages. The third model is a two‐target‐cell model taking into account the latently and actively infected cells. We have proven that if the basic reproduction number R 0 is less than unity, then the uninfected steady state is globally asymptotically stable, and if R 0 > 1, then the infected steady state is globally asymptotically stable. Copyright © 2012 John Wiley & Sons, Ltd.