Dynamic Analysis Of Two Classes Of Delayed HIV-1 Infection Models

In this thesis,by using the Hurwitz criterion?Lyapunov stability theory and LaSalle invariance principle,we study the dynamical behaviors of two kinds of HIV-1 infection models with time delay,which mainly include the positivity and boundedness,the stability of the equilibria.The results show that the basic reproduction number plays an important role in the stability of the equilibria.The dissertation consists of three chapters.In Chapter 1,the historical background and significance of AIDS research are in-troduced,and the research status of HIV dynamics is summarized.Finally,the main contents of this thesis and related knowledge that may be used are briefly introducedIn Chapter 2,a delayed HIV-1 infection model with eclipse stage and absorption effect is discussed.Firstly,We prove the positivity and boundedness of solutions.Then,by analyzing the corresponding characteristic equations of the equilibria,conditions for local stability of the equilibria are obtained.By using suitable Lyapunov functionals and the LaSalle invariance principle,the global stability of the infection-free equilibrium and sufficient condition for the global stability of the chronic-infection equilibrium arc derived Finally,Numerical simulations are given to verify our partial theoretical results.In Chapter 3,a delayed HIV-1 infection model with cell-to-cell transmission and immune impairment is constructed.First,the positivity,boundedness of solutions and the existence of the equilibria are discussed.Then,we calculate the basic reproduction number R0 and the immune response reproduction number R1.By constructing suitable Lyapunov functionals and using the LaSalle invariance principle,we study the global stability of the infection-free equilibrium and the immune-free infection equilibrium.For the immune infection equilibrium,we prove the global stability when ?=0.