In this work, we develop and analyze mathematical models for the coupled within-host and between-host dynamics caricaturing the evolution of HIV/AIDS. The host population is divided into susceptible, the infected without receiving treatment and the infected receiving ART treatment in accordance with China’s Four-Free-One-Care Policy. The within-host model is a typical ODE model adopted from literatures. The between-host model incorporates age-since-infection described by a system of integrodifferential equations. The two models are coupled via the viral load and number of CD4+ T cells of within the hosts. For the between-host model with an arbitrarily selected HIV infected individual, we focus on the analyses of the basic reproduction number R0 and the stabilities of equilibria. Through simulations we also find that the within-host dynamics does influence the between-host dynamics, and the nesting of within-host and between-host play a very important role in the HIV/AIDS evolution.
- Nested model