Global dynamics of a staged-progression model for HIV/AIDS with amelioration

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 R0R0. If R0≤1R0≤1, then the disease-free equilibrium (DFE) is globally asymptotically stable and the disease always dies out. If R0>1R0>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.