GLOBAL STABILITY FOR A CLASS OF DISCRETE SIR EPIDEMIC MODELS

被引：51
|
作者：
Enatsu, Yoichi [1 ]
Nakata, Yukihiko [1 ]
Muroya, Yoshiaki [2 ]
机构：
[1] Waseda Univ, Dept Pure & Appl Math, Shinjuku Ku, Tokyo 1698555, Japan
[2] Waseda Univ, Dept Math, Shinjuku Ku, Tokyo 1698555, Japan
来源：
MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2010年 / 7卷 / 02期
基金：
日本学术振兴会;
关键词：
Backward Euler method; discrete SIR epidemic model; distributed delays; globally asymptotic stability; Lyapunov functional; TIME-DELAY; COMPUTATION; DYNAMICS;
D O I：
10.3934/mbe.2010.7.347
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, we propose a class of discrete SIR epidemic models which are derived from SIR epidemic models with distributed delays by using a variation of the backward Euler method. Applying a Lyapunov functional technique, it is shown that the global dynamics of each discrete SIR epidemic model are fully determined by a single threshold parameter and the effect of discrete time delays are harmless for the global stability of the endemic equilibrium of the model.
引用
收藏
页码：347 / 361
页数：15
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