Study On Impulsive Delay HIV Model And Stochastic Delay SIS Model

In this paper,we consider the dynamic behavior of two kinds of infectious diseases.Firstly,we investigate a global dynamics of a delayed HIV epidemic model with switching parameters and impulsive control.We prove the existence and global attractivity of disease-free periodic solution and permanence of the disease.Secondly,we explore the susceptible-infectious-susceptible model.On the one hand,we establish the conditions for asymptotic equilibrium of the deterministic model and the globally asymptotic stability of the endemic equilibrium.On the other hand,the stochastic epidemic model with time delay is investigated and the sufficient conditions for the extinction and permanence of the system are obtained.In chapter one,we first introduce some background knowledge and present situation of the problems,and then introduce the theory of stochastic differential equation,time delay differential equation and impulsive differential equation.In chapter two,we investigate a global dynamics of a delayed HIV epidemic model with switching parameters and impulsive control.Firstly,applying the impulsive differential equation to the model,we obtain the existence and disease-free periodic solution and the global attractivity.Additionally,by using Ito formula,the threshold for permanance of the disease is obtained.Finally,some numerical simulations are provided to illustrate the theoretical results.In Chapter three,we build a deterministic infectious disease model.Firstly,we obtain the conditions for asymptotic equilibrium of the deterministic model and the globally asymptotic stability of the endemic equilibrium.Then the stochastic epidemic model with time delay is considered.By using Ito formula,we obtain the extinction and permanence of the system.While if the intensity of noise is very small,the population will be persistent,If the intensity of noise is sufficiently large,the population will go extinct.Finally,simulations are also carried out to illustrate our theoretical analysis.In chapter four,we summarize the main work of this paper and prospect our future work.