The Research On Dynamics Properties Of HIV Therapy Models With Impulsive Releasing Immune Factor

The research on mathematical models about HIV infection and treatments has a history nearly30years, among them, the vast majority of these models are based on the method of continuous dynamic system.However, in comparison, the pulse dynamical system can more accurately explain and simulation some biological phenomena in real life.Therefore, in this paper,we study two classes of models with HIV therapy of impulsive infusing immune factor in terms of the theory of impulsive differential equations, combining with the HIV therapies of infusing immune factor, and then get their corresponding dynamics properties respectively.This paper is composed of three chapters.Among them,In the first chapter, we mainly summarize the historical background and significance of HIV/AIDS research,research status of HIV infection and immune factor treatment models and the main work in this paper.In the second chapter,by using the stability theory of ordinary differential equations and the comparison theorem and Floquent multiplier theory of impulsive differential equations, we study a class of model with HIV therapy of pulse infusing immune factor. And firstly the stabilities of the equilibrium of the model, the existence and stability of the disease-free periodic solution are analyzed. Secondly, the cycle length of pulse infusion is estimated.Finally, by numerical simulations being performed,it is more intuitive to display the global asymptotic stability of periodic solutions of a impulsive differential system.In the third chapter,we improve the model on the basis of the second chapter.On the one hand, we consider the disease pathogenesis in a special period,that is the eclipse phase.On the other hand,we also consider the immune factor’s influence on the healthy cells and effective infected cells.So we build an HIV treatment model with impulsive infusing immune factor in the eclipse phase. In this chapter,by using the knowledge of the theory of impulsive differential equations, we obtain the conditions of the stabilities of equilibria, the existence of disease-free pulse periodic solution and the global asymptotic stability of this model. Finally the related numerical simulations are carried on.