带有外来移入人口的肺结核传染病模型

Epidemic Model with the Immigration Population

人口的流动会改变部分传染病的流行特点和发病规律,对疾病的控制带来一定的困难.设计一个带有外来移入人口的SEIR传染病模型,假设疾病的发生率是一个非线性单增函数,受患者数量的影响.通过对模型的分析,得出:系统没有无病平衡点,有唯一的地方病平衡点,证明了地方病平衡点是局部渐进稳定的,进一步研究了在恢复者获得永久性免疫的条件下,得到地方病平衡点的是全局渐进稳定性的唯一平衡点.

The immigration of population will have some effects on the epidemic characteristics of the infectious diseases. It will bring so much troubles to control it. A model to describe the infectious disease for immigration of population is proposed. In this model,the incidence rate of infectious disease is nonlinear increasing function and the epidemic speed of growth depends on the number of infections. By analysis of model there is no disease free equilibrium,but there is a unique endemic equilibrium which is locally asymptotically stable. The model with the recovery obtained permanent immunity is discussed further and the unique endemic equilibrium which is globally asymptotical stability is found out.