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GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA

李建全; 马知恩; 周义仓   

  1. 西安交通大学应用数学系, 西安 710049
  • 收稿日期:2003-06-23 修回日期:1900-01-01 出版日期:2006-01-20 发布日期:2006-01-20
  • 通讯作者: 李建全
  • 基金资助:

    Supported by the Nature Science Foundation of China(19971066) and Postdoctoral Foundation of China(2005037785).

GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA

Li Jianquan; Ma Zhien; Zhou Yicang   

  1. Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China
  • Received:2003-06-23 Revised:1900-01-01 Online:2006-01-20 Published:2006-01-20
  • Contact: Li Jianquan

摘要:

An SIS epidemic model with a simple vaccination is investigated in this article. The efficiency of vaccine, the disease-related death rate and population dynamics are also considered in this model. The authors find two threshold R0 and Rc (Rc may not exist). There is a unique endemic equilibrium for R0>1 or Rc=R0; there are two endemic equilibria for Rc0<1; and there is no endemic equilibrium for R0c<1. When Rc exists, there is a backward
bifurcation from the disease-free equilibrium for R0=1. They analyze the stability of equilibria and obtain the globally dynamic behaviors of the model. The results acquired in this article show that an accurate estimation of the efficiency of vaccine is necessary to prevent and controll the spread of disease.

关键词: Epidemic model, equilibrium, backwards bifurcation, vaccination, stability

Abstract:

An SIS epidemic model with a simple vaccination is investigated in this article. The efficiency of vaccine, the disease-related death rate and population dynamics are also considered in this model. The authors find two threshold R0 and Rc (Rc may not exist). There is a unique endemic equilibrium for R0>1 or Rc=R0; there are two endemic equilibria for Rc0<1; and there is no endemic equilibrium for R0c<1. When Rc exists, there is a backward
bifurcation from the disease-free equilibrium for R0=1. They analyze the stability of equilibria and obtain the globally dynamic behaviors of the model. The results acquired in this article show that an accurate estimation of the efficiency of vaccine is necessary to prevent and controll the spread of disease.

Key words: Epidemic model, equilibrium, backwards bifurcation, vaccination, stability

中图分类号: 

  • 34D23