ON THE GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DISTRIBUTED DELAYS

被引：0
|
作者：
Nakata, Yukihiko [1 ]
Enatsu, Yoichi [2 ]
Muroya, Yoshiaki [3 ]
机构：
[1] Basque Ctr Appl Math, Bizkaia Technol Pk,Bldg 500, E-48160 Derio, Spain
[2] Waseda Univ, Dept Pure & Appl Math, Shinjuku Ku, Tokyo 1698555, Japan
[3] Waseda Univ, Dept Math, Shinjuku Ku, Tokyo 1698555, Japan
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2011年 / 31卷
基金：
日本学术振兴会;
关键词：
SIRS epidemic model; global asymptotic stability; distributed delays; Lyapunov functional;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish the global asymptotic stability of an endemic equilibrium for an SIRS epidemic model with distributed time delays. It is shown that the global stability holds for any rate of immunity loss, if the basic reproduction number is greater than 1 and less than or equals to a critical value. Otherwise, there is a maximal rate of immunity loss which guarantees the global stability. By using an extension of a Lyapunov functional established by [C.C. McCluskey, Complete global stability for an SIR epidemic model with delay -Distributed or discrete, Nonlinear Anal. RWA. 11 (2010) 55-59], we provide a partial answer to an open problem whether the endemic equilibrium is globally stable, whenever it exists, or not.
引用
收藏
页码：1119 / 1128
页数：10
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