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Mathematical analysis of the global dynamics of a model for HIV infection of CD4$^{+}$ T cells. (English) Zbl 1086.92035
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:
92C60Medical epidemiology
34D05Asymptotic stability of ODE
34D23Global stability of ODE
37N25Dynamical systems in biology
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References:
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