文章基本信息

标题：Bifurcations for a deterministic SIR epidemic model in discrete time
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作者：Xiaoliang Zhou ; Xiaopei Li ; Wu-Sheng Wang 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：168
DOI：10.1186/1687-1847-2014-168
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we are concerned with the theoretical analysis of the bifurcations for a deterministic SIR epidemic model in discrete time. By deriving equations describing flows on the center manifolds, we discuss the transcritical bifurcation at the disease-free equilibrium point and the direction and stability of the flip bifurcation at the positive endemic equilibrium point. We give explicit conditions to check the stability of equilibrium points and the critical parameter for the emergence of a flip bifurcation. For illustrating the theoretical analysis, we also give some numerical simulation examples. MSC:37N25, 39A11, 92B05.
关键词：center manifold ; discrete time ; epidemic model ; flip bifurcation ; transcritical bifurcation