Electronic Journal of Differential Equations,
Vol. 2015 (2015), No. 33, pp. 1-19.

Title: Mathematical analysis for an age-structured HIV infection model 
       with saturation infection rate

Authors: Jinliang Wang (Heilongjiang Univ.,  Harbin, China)
         Ran Zhang     (Heilongjiang Univ.,  Harbin, China)
         Toshikazu Kuniya (Kobe Univ., Japan)

Abstract:
 In this article, we study a continuous age-structured HIV infection model.
 For the case of the saturation infection rate, the basic reproduction number
 $\Re_0$ is shown to be a sharp threshold value for the global  dynamics;
 that is, the infection-free equilibrium is globally stable if $\Re_0 < 1$,
 while a unique infection equilibrium is so if $\Re_0 > 1$.
 For the proof, we use Lyapunov functional techniques based on the relative
 compactness of the orbit and uniform persistence of the system.

Submitted April 25, 2014. Published February 06, 2015.
Math Subject Classifications: 92D30, 34D23, 34K20.
Key Words: Age-infection model; nonlinear incidence rate;
           relative compactness;  uniform persistence; Lyapunov function.