The Nonlinear Rate And Stage Structure Of The Infectious Disease Model

Infectious diseases have always been the enemy of human health , in the history ,theprevalence of infectious diseases has brought great disaster to human survival and people'slivelihood again and again .Therefore, the study of infectious diseases has always been subjectto people's concern.We focus the research of a infectious disease model on its balance offeatures and threshold conditions, including local stability, global stability, persistence, Hopfbranches and so on.In this paper we focus on the following aspects:In the first chapters I and II, we mainly introduces the research significance of infectiousdiseases, research history, and the basic concepts and theorems related to this article.In the third chapter, we analyze and formulate the delayed SIR epidemic model withnonlinear incidence rate ,through the analysis of the characteristic equation ,we show thatdisease-free equilibrium and positive equilibrium is locally asymptotically stability.And then,we show that the two equilibriums are globally asymptotically stability.In the fourth chapter, we analyze the epidemic model with stage structure and saturationincidence rate .we get the basic reproduction number and equilibriums, through the analysisof the characteristic equation,we can get the locally asymptotically stable condition of thedisease-free equilibrium and endermic equilibrium,and get the global stability conditions ofthe equilibriums by constructing appropriate Lyapunov functions and Dulac functions.atlast,we illustrate the results with numerical simulations.In the fifth chapter, we analyze the epidemic model with stage structure and verticaltransmission ,the period of infection is partitioned into the early and later stages, throughthe analysis ,we can prove that the system is locally and globally asymptotically stable withdisease-related death.