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Global properties of a class of HIV infection models with Beddington-DeAngelis functional response. (English) Zbl 06163079
Summary: 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.
MSC:
34A34Nonlinear ODE and systems, general
34D23Global stability of ODE
92B05General biology and biomathematics
92C60Medical epidemiology