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

作　　者：张娟 李建全 马知恩 

机构地区：[1]Department of Mathematics Xi'an Jiaotong University,Xi'an 710049,China

出　　处：《Acta Mathematica Scientia》2006年第3期551-567,共17页数学物理学报（B辑英文版）

基　　金：This research is supported by the NNSF of China (19971066)

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.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.

关 键 词：SEIR model population size dependent contact rate COMPARTMENT infected individual compound matrix 

分 类 号：O29[理学—应用数学]