Mathematical Analysis for an Age-structured Hiv Infection Model with Saturation Infection Rate

In this article, we study a continuous age-structured HIV infection model. For the case of the saturation infection rate, the basic reproduction number <0 is shown to be a sharp threshold value for the global dynamics; that is, the infection-free equilibrium is globally stable if <0 < 1, while a unique infection equilibrium is so if <0 > 1. For the proof, we use Lyapunov functional techniques based on the relative compactness of the orbit and uniform persistence of the system.