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.