An Epidemic Model Analysis With Population Dispersal And Entry Screening

Epidemic models is used to be studied the mechanism of diease transmission. In this paper, by analysizing the dynamic nature of a class of epidemic models, we can use it to describe the dynamics of disease spread among patches. And by using analyze the dynamic nature of a class of epidemic models, we discusse how do these various parameters effect the spread and curing dynamic condition of this infectious disease.The model which we studied in this article is a multi-dimensional model, we found that the model has four equations playing an important role in the entire system. So it could consider separately. The system which composed the four equations has reflected the whole system of nature, therefore, mainly by the study of the four equation to study the entire system. And through the study of the disease-free equilibrium and the positive equilibrium of the existence and stability of the system, we particular analyzed the system of detailed global properties.We mainly discuss the following work:First of all, we establish a threshold above which the disease is uniformly persistent and below which disease-free equilibrium is locally attractive. Secondly, by adjective matrix and some basic knowledge of dynamic system, we analyze stability of positive equibilriums in the models.Thirdly, the system is globally attractive when both susceptible and infective individuals in each patch have the same disperal rate.Finally, the population dispersal plays an important roal for the disease spread. The population dispersal induces the spread of the disease in all patches, even though the disease can not spread in each isolated patch.