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Zbl 1197.34073
Elaiw, A.M.
Global properties of a class of HIV models. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 4, 2253-2263 (2010). ISSN 1468-1218

Summary: We study the global properties of a class of human immunodeficiency virus (HIV) models. The basic model is a 5-dimensional nonlinear ODEs that describes the interaction of the HIV with two target cells, CD4$^{+}$ T cells and macrophages. An HIV model with exposed state and a model with nonlinear incidence rate are also analyzed. Lyapunov functions are constructed to establish the global asymptotic stability of the uninfected and infected steady states. We have proven that if the basic reproduction number $R_{0}$ is less than unity, then the uninfected steady state is globally asymptotically stable. If $R_{0}>1$ (or if the infected steady state exists), then the infected steady state is globally asymptotically stable. In a control system framework, we have shown that the HIV model incorporating the effect of Highly Active AntiRetroviral Therapy (HAART) is globally asymptotically controllable to the uninfected steady state.

MSC 2000:: *34C60 Applications of qualitative theory of ODE
92D30 Epidemiology
92C60 Medical epidemiology
34D05 Asymptotic stability of ODE
34D20 Lyapunov stability of ODE
34H05 ODE in connection with control problems

Keywords: global stability; direct Lyapunov method; HIV/AIDS; controllability

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Zentralblatt MATH Berlin [Germany]