Study On The Dynamics Of Epidemic Model And Impulsive Differential Systems

The result of this dissertation can be summarized as following:In chapter one, the stability of SIR epidemic model with vaccinal immunity and a varying total population size is studied. The basic reproductive numberσis found which determines the existence of infective disease. In some conditions, we demonstrate that the disease free equilibrium is globally stable. The existence of a unique endemic equilibrium and the condition of local asymptotic stability are obtained. For the important cases of bilinear and standard incidence of infection, global asymptotic stability of the endemic equilibrium are proved provided the basic reproduction number is more than unity. Some existed results are not only extended but also improved.In chapter two, we establish a kind of new class age-structure SEIR epidemic model with impulsive vaccination and nonlinear infectivity, which contains ODEs and PDEs at the same time. We demonstrate that the disease-free periodic solution is a global attractor if the reproductive number of infective is less than one.In the third chapter, our main purpose is to construct a three trophic level food chain system with Holling IV functional responses and periodic constant impulsive effect concerning integrated pest management (IPM), and investigate the dynamic behaviors of this system. By using the Floquet theory and comparison theorem of impulsive differential equation, Liapunov function and analytic method, we prove that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Further, condition for permanence of the system is established. Finally, we conclude that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently.