Global Stability for a Heroin Model with Age-Dependent Susceptibility

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 deter...

Full description

Saved in:
Bibliographic Details
Published inJournal of systems science and complexity Vol. 28; no. 6; pp. 1243 - 1257
Main Authors Fang, Bin, Li, Xuezhi, Martcheva, Maia, Cai, Liming
Format Journal Article
LanguageEnglish
Published Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.12.2015
Subjects
Complex Systems
Control
Lyapunov函数
Lyapunov方法
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Statistics
Systems Theory
Volterra型
依赖性
全局稳定性
年龄结构
海洛因
结构模型
global stability
equilibrium
Age-structured
heroin model
basic reproduction number
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:Age-structured,basic reproduction number,equilibrium,global stability,heroin model
11-4543/O1
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.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-015-3243-9