Dynamical behavior of an epidemic model with a nonlinear incidence rate

被引:499
作者
Ruan, SG
Wang, WD
机构
[1] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada
[2] SW Normal Univ, Dept Math, Chongqing 400715, Peoples R China
基金
加拿大自然科学与工程研究理事会; 中国国家自然科学基金;
关键词
epidemic; nonlinear incidence; global analysis; bifurcation; limit cycle;
D O I
10.1016/S0022-0396(02)00089-X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we study the global dynamics of an epidemic model with vital dynamics and nonlinear incidence rate of saturated mass action. By carrying out global qualitative and bifurcation analyses, it is shown that either the number of infective individuals tends to zero as time evolves or there is a region such that the disease will be persistent if the initial position lies in the region and the disease will disappear if the initial position lies outside this region. When such a region exists, it is shown that the model undergoes a Bogdanov-Takens bifurcation, i.e., it exhibits a saddle-node bifurcation, Hopf bifurcations, and a homoclinic bifurcation. Existence of none, one or two limit cycles is also discussed. (C) 2002 Elsevier Science (USA). All rights reserved.
引用
收藏
页码:135 / 163
页数:29
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