GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS

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...

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Bibliographic Details
Published inActa Mathematica Scientia Vol. 26; no. 3; pp. 551 - 567
Main Author 张娟 李建全 马知恩
Format Journal Article
LanguageEnglish
Published 01.07.2006
Subjects
混合矩阵
种群尺寸相依接触率
预知模型
compartment
SEIR model
infected individual
compound matrix
population size dependent contact rate
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ISSN0252-9602
1572-9087
1003-3998
DOI10.1016/S0252-9602(06)60081-7

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Summary: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.
Bibliography:O151.21
SEIR model, population size dependent contact rate, compartment, infected individual, compound matrix
42-1227/O
ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0252-9602
1572-9087
1003-3998
DOI:10.1016/S0252-9602(06)60081-7