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Zbl 1086.92035
Wang, Liancheng; Li, Michael Y.
Mathematical analysis of the global dynamics of a model for HIV infection of CD4$^{+}$ T cells. (English)
[J] Math. Biosci. 200, No. 1, 44-57 (2006). ISSN 0025-5564

Summary: A mathematical model that describes HIV infection of CD4$^{+}$ T cells is analyzed. Global dynamics of the model is rigorously established. We prove that, if the basic reproduction number $R_{0}\le 1$, the HIV infection is cleared from the T-cell population; if $R_{0} > 1$, the HIV infection persists. For an open set of parameter values, the chronic-infection equilibrium $P^*$ can be unstable and periodic solutions may exist. We establish parameter regions for which $P^*$ is globally stable.

MSC 2000:: *92C60 Medical epidemiology
34D05 Asymptotic stability of ODE
34D23 Global stability
37N25 Dynamical systems in biology

Keywords: HIV infection; CD4$^{+}$ T cells; dynamical systems; stability analysis

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Zentralblatt MATH Berlin [Germany]