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
is shown to be a sharp threshold value for the global dynamics;
that is, the infection-free equilibrium is globally stable if
,
while a unique infection equilibrium is so if
.
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 |
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Ran Zhang School of Mathematical Science Heilongjiang University Harbin 150080, China email: ranzhang90@aliyun.com |
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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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