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Global dynamics of a staged-progression model for HIV/AIDS with amelioration. (English) Zbl 1225.34052
Summary: We consider a mathematical model for HIV/AIDS that incorporates staged progression and amelioration. Amelioration as a result of HAART treatment is allowed to occur across any number of stages. The global dynamics are completely determined by the basic reproduction number \(R_{0}\). If \(R_{0}\leq 1\), then the disease-free equilibrium (DFE) is globally asymptotically stable and the disease always dies out. If \(R_{0}>1\), DFE is unstable and a unique endemic equilibrium (EE) is globally asymptotically stable, and the disease persists at the endemic equilibrium. The proof of global stability utilizes a global Lyapunov function.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
92C60 Medical epidemiology
34D20 Stability of solutions to ordinary differential equations
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