Global stability of an infection-age structured HIV-1 model linking within-host and between-host dynamics

Although much evidence shows the inseparable interaction between the within-host progression of HIV-1 infection and the transmission of the disease at the population level, few models coupling the within-host and between-host dynamics have been developed. In this paper, we adopt the nested approach, viewing the transmission rate at each stage (primary, chronic, and AIDS stage) of HIV-1 infection as a saturated function of the viral load, to formulate an infection-age structured epidemic model. We explicitly link the individual and the host population scale, and derive the basic reproduction number R0 for the coupled system. To analyze the model and perform a detailed global dynamics analysis, two Lyapunov functionals are constructed to prove the global asymptotical stability of the disease-free and endemic equilibria. Theoretical results indicate that R0 provides a threshold value determining whether or not the disease dies out. Numerical simulations are presented to quantitatively investigate the influence of the within-host viral dynamics on between-host transmission dynamics. The results suggest that increasing the effectiveness of inhibitors can decrease the basic reproduction number, but can also increase the overall infected population because of a lower disease-induced mortality rate and a longer lifespan of HIV infected individuals.