Study On Some Epidemic Models With Latency

In this paper, there are four chapters. The preface is in chapter 1, we introduce some knowledge of Epidemic models, the main work and concept and conclusion that is used.In Chapter 2, we introduce and study the epidemic model of pulse vaccination with delay and nonlinear incidence. We investigate the exis-tence and global attractiveness of the infection-free period solutions of the system. By using the theory on delay functional and impulsive differen-tial equation,we obtain the sufficient condition for the permanence of the system.In Chapter 3, we study an SIR model with periodic vertical infection rate. The dynamical behavior of the model is analyzed. For the model in the small amplitude, we give the approximate expression of the periodic solution and show that the periodic solution is stable. The numerical simulation supports our conjecture.In Chapter 4, we establish and analyze an SEIR Model that incorpo-rates saturating incidence and the disease infectivity in the latency. The basic reproduction number R0 is obtained for the model, and the suffi-cient condition that the disease free equilibrium and the unique endemic equilibrium are globally asymptotically stable is derived.