| GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA |
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| 作者姓名： | 李建全 马知恩 周义仓 |
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| 作者单位： | Department of Applied Mathematics Xi'an Jiaotong University，Department of Applied Mathematics Xi'an Jiaotong University，Department of Applied Mathematics Xi'an Jiaotong University Xi'an 710049，China Telecommunication Engineering Institute，Air Force Engineering University，Xi'an 710077，China，Xi'an 710049，China，Xi'an 710049，China |
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| 基金项目： | Supported by the Nature Science Foundation of China(19971066)
Postdoctoral Foundation of China(2005037785) |
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| 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 Rc < R0 < 1; and there is no endemic equilibrium for R0 < Rc < 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.
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| 关 键 词： | 传染模型 平衡性 分歧理论 稳定性 |
| 收稿时间： | 2003-06-23 |
GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA |
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| Li Jianquan,Ma Zhien,Zhou Yicang.GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA[J].Acta Mathematica Scientia,2006,26(1):83-93. |
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| Authors: | Li Jianquan Ma Zhien Zhou Yicang |
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| 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 Rc < R0 < 1; and there is no endemic equilibrium for R0 < Rc < 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. |
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| Keywords: | Epidemic model equilibrium backwards bifurcation vaccination stability |
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