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Global stability for a heroin model with age-dependent susceptibility

被引：26
|
作者：
Fang, Bin [1 ,2 ]
Li, Xuezhi [1 ]
Martcheva, Maia [3 ]
Cai, Liming [1 ]
机构：
[1] Xinyang Normal Univ, Dept Math, Xinyang 464000, Peoples R China
[2] Beijing Inst Informat & Control, Beijing 100037, Peoples R China
[3] Univ Florida, Dept Math, Gainesville, FL 32611 USA
来源：
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2015年 / 28卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Age-structured; basic reproduction number; equilibrium; global stability; heroin model; EPIDEMIC MODEL; USERS;
D O I：
10.1007/s11424-015-3243-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper considers global asymptotic properties for an age-structured model of heroin use based on the principles of mathematical epidemiology where the incidence rate depends on the age of susceptible individuals. The basic reproduction number of the heroin spread is obtained. It completely determines the stability of equilibria. By using the direct Lyapunov method with Volterra type Lyapunov function, the authors show that the drug-free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and the unique drug spread equilibrium is globally asymptotically stable if the basic reproduction number is greater than one.
引用
收藏
页码：1243 / 1257
页数：15
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