Global dynamics for a class of age-infection HIV models with nonlinear infection rate

In this paper, we study the global stability of a class of HIV viral infection models with continuous age-structure using the direct Lyapunov method. In each of the cases where the incidence rates are given by nonlinear infection rate F(T)G(V)F(T)G(V), Holling type II functional response and Crowley–Martin functional response, we define the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not. We give a rigorous mathematical analysis on technical materials and necessary arguments, including relative compactness of the orbit and uniform persistence of system, by reformulating the system as a system of Volterra integral equations. We further investigate global behaviors of HIV viral infection models with Holling type II functional response and Crowley–Martin functional response through numerical simulations.