Global threshold dynamics of an HIV/AIDS model with multi-class-age structure.

Given that HIV/AIDS infection is characterized by long and variable periods of infectiousness, variable infectivity, and age heterogeneity, this work focuses on the global behavior of a PDE HIV/AIDS model structured by ages of susceptibility, treatment, and multi-stage infection. Local stability of the model is demonstrated. Its uniform persistence is ingeniously solved. Particularly, global asymptotic stability of unique positive equilibrium is addressed by a concise method in which the highlight lies in determining the 'kernel function' in the Lyapunov functional to derive the semi-negative definiteness of its time derivative. Numerical experiments are also shown to reinforce our theoretical results. These results can contribute to a better understanding of the impacts of class age on the evolution of AIDS in a population and inform the development of AIDS prevention strategies. [ABSTRACT FROM AUTHOR]