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), 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. (C) 2015 Elsevier Inc. All rights reserved.