Stability and bifurcation of an SIR epidemic model with nonlinear incidence and treatment

被引：68
作者：
Li, Xue-Zhi [1 ]
Li, Wen-Sheng [1 ,2 ]
Ghosh, Mini [3 ]
机构：
[1] Xinyang Normal Univ, Dept Math, Xinyang 464000, Peoples R China
[2] Fugou Middle Sch, Fugou 461300, Henan Province, Peoples R China
[3] Thapar Univ, Sch Math & Comp Applicat, Patiala 147004, Punjab, India
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 210卷 / 01期
基金：
中国国家自然科学基金;
关键词：
SIR epidemic model; Treatment; Nonlinear incidence rate; Backward bifurcation; Stability;
D O I：
10.1016/j.amc.2008.12.085
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The dynamical behaviors of an SIR epidemic model with nonlinear incidence and treatment is investigated. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low. Theoretical and numerical results suggest that decreasing the basic reproduction number below one is insufficient for disease eradication. (C) 2009 Elsevier Inc. All rights reserved.
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页码：141 / 150
页数：10
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