Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model

被引：85
作者：
Enatsu, Yoichi [1 ]
Nakata, Yukihiko [2 ]
Muroya, Yoshiaki [3 ]
机构：
[1] Waseda Univ, Dept Pure & Appl Math, Shinjuku Ku, Tokyo 1698555, Japan
[2] Basque Ctr Appl Math, E-48009 Bilbao, Spain
[3] Waseda Univ, Dept Math, Shinjuku Ku, Tokyo 1698555, Japan
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2012年 / 13卷 / 05期
基金：
日本学术振兴会;
关键词：
SIRS epidemic model; Nonlinear incidence rate; Global asymptotic stability; Lyapunov functional; Distributed delays; BEHAVIOR;
D O I：
10.1016/j.nonrwa.2012.01.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the global dynamics of a delayed SIRS epidemic model for transmission of disease with a class of nonlinear incidence rates of the form beta S(t) integral(h)(0), f(tau)G(I(t - tau))d tau. Applying Lyapunov functional techniques in the recent paper [Y. Nakata, Y. Enatsu, Y. Muroya, On the global stability of an SIRS epidemic model with distributed delays, Discrete Contin. Dyn. Syst. Supplement (2011) 1119-1128], we establish sufficient conditions of the rate of immunity loss for the global asymptotic stability of an endemic equilibrium for the model. In particular, we offer a unified construction of Lyapunov functionals for both cases of R-0 <= 1 and R-0 > 1, where R-0 is the basic reproduction number. (C) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2120 / 2133
页数：14
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