Permanence And Periodic Solution Of Several Epidemic Models With Pulse Vaccination

Mathematical models of differential equations play an important role in describing population dynamic behavior.Especially,impulsive differential equations describe population dynamic models,which is more reasonable and precise on reflecting all kinds of change orderliness,since many life phenomena and human exploitation are almost impulsive in the natural world.In this dissertation,population dynamic models are established to control infection by means of the theory and method of impulsive differential equations.Numerical simulations are used to investigate dynamic behavior including the existence of periodic solution,the permanence and infection free periodic solution.The main results of this dissertation may be summarized as follows:The differential susceptibility SIR epidemic model with time delay and pulse vaccination are considered in Chapter 3.The dynamics of the epidemic model is globally investigated by using comparison theorem of impulsive differential equation and analytic method.We obtain the conditions of global attractivity of infection-free periodic solution and permanence.When epidemic models are constructed to describe the transmission of infectious diseases,the immature and mature have different susceptibility,which are not always neglected.Compared with the epidemic models without stage structure,the epidemic models with stage structure can describe the features of the diseases diffusion more well and truly.In Chapter 3,we propose the differential susceptibility SIR epidemic model with stage structure and pulse vaccination.Due to the coexistence of time delays and stage structure,the dynamical behaviors become more complex and are difficult to study,we analyze and study the model.We obtain the conditions of global attractivity of infection-free periodic solution and permanence.In Chapter 4,we propose a delayed SIRS epidemic model with non-monotonic incidence rate and pulse vaccination,we analyze and study the model.We obtain the conditions of global attractivity of infection-free periodic solution and permanence.