The Study Of Two Kinds Of Infectious Disease Model With Satu-Rated Time Delay Incidence Rate

This paper studies the dynamics of two types of epidemic model with saturation inci-dence Delays,One study was SQIR model with isolated items, another study SIRS Epidemic Model.Based on the literature have been many new conclusions. The first chapter is introduc-tion, which mainly explains the research background, the main task of the thesis and some important preliminaries.The second chapter, which mainly establishes a saturated Delays incidence SQIR epidemic model,the main items discussed in isolation and with a saturated incidence of infectious diseases In this section, using the method of analysis and Routh Hurwitz criterion discussed existence and locally asymptotic stability of the two equilibrium point; And discusses the permanence of the system, obtained the sufficient condition of persistent; Then, by constructing suitable lyapunov function V (t) study the global stability of the equilibrium.The third chapter,which mainly establishes a saturated Delays incidence SIRS epidemic model,the main items discussed in isolation and with a saturated incidence of infectious diseases In this section, using the method of analysis and Routh Hurwitz criterion discussed existence and locally asymptotic stability of the two equilibrium point; And discusses the permanence of the system, obtained the sufficient condition of persistent; Then, by constructing suitable lyapunov function V (t) study the global stability of the equilibrium.