一类带移民输入的传染病动力学行为分析

研究了一类带移民输入、免疫和接触率依赖于人口数量的SEIRS模型,其中移民包含易感者、潜伏者、感染者和康复者。通过推导得系统存在一个地方病平衡点,并用极限方程和复合矩阵的有关理论在三维空间中证明了地方病平衡点的全局渐进稳定性。如果所有移民都是易感者,将得到一个平衡点稳定的阈值。

Dynamic Analysis of an Epidemic Model with Constant Immigration and Immunity

This article has considered an SEIRS model that incorporates the constant inflow of new individuals.The model also incorporates a population size dependent contact rate.The constant inflow includes susceptible,exposed,infected person and rehabilitation clients.As the infected fraction cannot be eliminated from the population,it was identifiecd that there is an endemic equilibrium which is globally asymptotically stable.In order to prove the global asymptotical stability of the endemic equilibrium,the system was changed into a three-dimensional asymptotical autonomous system with limit equation.If immigrants are all susceptible,the model considered here shows a threshold phenomenon and a sharp threshold has been obtained.