Electron. J. Diff. Equ., Vol. 2015 (2015), No. 33, pp. 1-19.

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

Jinliang Wang, Ran Zhang, Toshikazu Kuniya

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 6, 2015.
Math Subject Classifications: 92D30, 34D23, 34K20.
Key Words: Age-infection model; nonlinear incidence rate; relative compactness; uniform persistence; Lyapunov function.

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Jinliang Wang
School of Mathematical Science
Heilongjiang University
Harbin 150080, China
email: jinliangwang@hlju.edu.cn
Ran Zhang
School of Mathematical Science
Heilongjiang University
Harbin 150080, China
email: ranzhang90@aliyun.com
Toshikazu Kuniya
Graduate School of System Informatics
Kobe University, 1-1 Rokkodai-cho
Nada-ku, Kobe 657-8501, Japan
email: tkuniya@port.kobe-u.ac.jp

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