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Zbl 1225.34052
Guo, Hongbin; Li, Michael Y.
Global dynamics of a staged-progression model for HIV/AIDS with amelioration.
(English)
[J] Nonlinear Anal., Real World Appl. 12, No. 5, 2529-2540 (2011). ISSN 1468-1218

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 2000:
*34C60 Applications of qualitative theory of ODE
92C60 Medical epidemiology
34D20 Lyapunov stability of ODE

Keywords: staged progression; HIV/AIDS; amelioration; basic reproduction number; global stability; Lyapunov functions

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