| GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS |
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| 作者姓名： | 张娟 李建全 马知恩 |
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| 作者单位： | Department of Mathematics Xi'an Jiaotong University Xi'an 710049，China，Department of Mathematics Xi'an Jiaotong University，Xi'an 710049，China，Department of Mathematics Xi'an Jiaotong University，Xi'an 710049，China |
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| 基金项目： | This research is supported by the NNSF of China (19971066) |
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| 摘 要： | The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.
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| 关 键 词： | 预知模型 种群尺寸相依接触率 间隔 混合矩阵 |
| 收稿时间： | 2004-10-31 |
GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS |
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| Zhang Juan, Li Jianquan, Ma Zhien.GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS[J].Acta Mathematica Scientia,2006,26(3):551-567. |
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| Authors: | Zhang Juan Li Jianquan Ma Zhien |
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| Abstract: | The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation. |
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| Keywords: | SEIR model population size dependent contact rate compartment infected individual compound matrix |
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