GLOBAL STABILITY FOR A HEROIN MODEL WITH TWO DISTRIBUTED DELAYS

被引：39
作者：
Fang, Bin [1 ,2 ]
Li, Xuezhi [2 ]
Martcheva, Maia [3 ]
Cai, Liming [2 ]
机构：
[1] Beijing Inst Informat & Control, Beijing 100037, Peoples R China
[2] Xinyang Normal Univ, Dept Math, Xinyang 464000, Peoples R China
[3] Univ Florida, Dept Math, Gainesville, FL 32611 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2014年 / 19卷 / 03期
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
Heroin model; distributed delay; basic reproduction number; Lyapunov function; global stability; EPIDEMIC; USERS;
D O I：
10.3934/dcdsb.2014.19.715
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider global stability for a heroin model with two distributed delays. The basic reproduction number of the heroin spread is obtained, which completely determines the stability of the equilibria. Using the direct Lyapunov method with Volterra type Lyapunov function, we show that the drug use-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：715 / 733
页数：19
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