The Study Of Some Classes Of Epidemic Models With Nonlinear Incidence Rate

The paper focuses on epidemic models with nonlinear incidence rate, It consists of four chapters.In Chapter 1, the significance of the research and the structure of the thesis is briefly introduce.In Chapter 2, the impulsive delay epidemic model with nonlinear incidence ?ISq and two parallel infectious stage is considered. By using the comparison principle, the global attractivity of infection-free periodic solutions is verified when R1< 1 and R2< 1, and a sufficient condition for the permanence of the epidemic is also given when R3> 1 and R4>1.In Chapter 3, the kind of epidemic model with nonlinear incidence rate ?I(1+vIk-1)S and impulsive vaccination is considered, and the kind of SEIRS delay epidemic model with latent periods is discussed. Applying the comparison theorem in impulsive differential equation and the analytical method, the global attractiveness of the disease-free periodic solutions is obtained, and sufficient condition is obtained for the permanence of the system.In Chapter 4, by using Lyapunov function and the comparison principle, the kind of SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination is formu-lated, the global attractivity of infection-free periodic solutions is obtained when Ri*< 1, and the permanence of the epidemic is given when R2*> 1.