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

页码：2120 / 2133

页数：14

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