The Study On Epidemic Models With Stage Of Infection

In this paper, some epidemic models with stage of infection are stud-ied. The asymptotic behavior of solutions of the systems'is analyzed. The article is divided into four chapters.In Chapter 1, the background of this topic and some relative litera-tures are presented.In Chapter 2, we study an epidemic model with saturated incidence rate and the effect of the infected refuges. The sufficient conditions for the local stability of the disease-free equilibrium and the endemic equilibrium are obtained. The global stability conditions are also achieved. The effect of refuges on the stability of the positive equilibrium is also carried on, and our results show that refuge can hold back the disease.In Chapter 3, we study the SIVR epidemic model with stage of infec-tion and precautionary vaccination. First, an SIVR epidemic model with stage of infection and continually precautionary vaccination are discussed. By using the stability theory for ordinary differential equations, we obtain the global asymptotical stability conditions of the disease-free equilibrium and the endemic equilibrium, give the basic reproduction number R0. Sec-ond, the SIVR epidemic model with stage of infection and pulse vaccination are discussed. The existence of disease-free periodic solution is obtained by using the theory of fixed point, the sufficient conditions for the disease-free periodic solution is globally asymptotical stability is obtained by using the Floquet theory of impulsive equations and comparison theorem.In Chapter 4, we study an SIVS epidemic model with standard in-cidence rate and quad acute and chronic stage, the global asymptotical stability conditions for the disease-free equilibrium and the endemic equi-librium are obtained, give the basic reproduction number R0.