Backward bifurcation of an epidemic model with standard incidence rate and treatment rate

被引：49
|
作者：
Hu, Zhixing [1 ]
Liu, Sheng [2 ]
Wang, Hui [1 ]
机构：
[1] Univ Sci & Technol Beijing, Dept Appl Math & Mech, Beijing 100083, Peoples R China
[2] Beijing Forestry Univ, Sch Sci, Beijing 100083, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2008年 / 9卷 / 05期
关键词：
epidemic model; treatment; standard incidence rate; backward bifurcation;
D O I：
10.1016/j.nonrwa.2007.08.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An epidemic model with standard incidence rate and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infectives on the disease spread. It is assumed that treatment rate is proportional to the numbers of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infectives. 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. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2302 / 2312
页数：11
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