Local stability of an SIR epidemic model and effect of time delay

被引：12
|
作者：
Tchuenche, Jean M. [1 ]
Nwagwo, Alexander [2 ]
机构：
[1] Univ Dar Es Salaam, Dept Math, Dar Es Salaam, Tanzania
[2] Univ Ibadan, Dept Math, Ibadan, Nigeria
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2009年 / 32卷 / 16期
关键词：
SIR model; time delay; Lyapunov function; local stability; GLOBAL STABILITY;
D O I：
10.1002/mma.1136
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We describe an SIR epidemic model with a discrete time lag, analyse the local stability of its equilibria as well as the effects of delay on the reproduction number and on the dynamical behaviour of the system. The model has two equilibria-a necessary condition for local asymptotic stability is given. The proofs are based on linearization and the application of Lyapunov functional approach. An upper bound of the critical time delay for which the model remains valid is derived. Numerical simulations are carried out to illustrate the effect of time delay which tends to reduce the epidemic threshold. Copyright (C) 2009 John Wiley & Sons, Ltd.
引用
收藏
页码：2160 / 2175
页数：16
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