Global stability of the endemic equilibrium of a discrete SIR epidemic model

被引：0
|
作者：
Xia Ma
Yicang Zhou
Hui Cao
机构：
[1] Xi’an Jiaotong University,Department of Applied Mathematics
[2] Shaanxi University of Science & Technology,School of Science
来源：
Advances in Difference Equations | / 2013卷
关键词：
discrete SIR model; global stability; asymptotic behavior; persistence;
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学科分类号：
摘要：
The basic reproductive number R0 of a discrete SIR epidemic model is defined and the dynamical behavior of the model is studied. It is proved that the disease free equilibrium is globally asymptotically stable if R0<1, and the persistence of the model is obtained when R0>1. The main attention is paid to the global stability of the endemic equilibrium. Sufficient conditions for the global stability of the endemic equilibrium are established by using the comparison principle. Numerical simulations are done to show our theoretical results and to demonstrate the complicated dynamics of the model.
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