The Study Of Two Classes Of HIV Models With Delays

In this paper,we mainly study the dy-namics of two classes of HIV models with delays.The article includes three chapters.The preface is in chapter 1,we introduce the research background of this article and some important,preliminaries.In Chapter 2,we propose and analyze a delayed HIV model with both virus-to-cell and cell-to-cell transmissions.Firstly,the basic reproduction number R0 and the immune-activated reproduction number R1 are obtained.Secondly,we obtain the existence of three equilibria,the infection-free equilibrium E0,the immune-exhausted equilibrium E1,and the endemic equi-librium E2,respectively.Thirdly,by constructing suitable Lyapunov functionals and by using LaSalle's invariance principle,we get that the stability of the equilibria.In addition,numerical simulations are carried out to illustrate the theoretical results.In Chapter 3.we formulate a HIV-1 model with diffusion and time delay.Firstly,The globally stability analysis of the model is carried out in terms of the basic reproduction number R0 using Lyapunov functionals.Secondly,sufficient conditions for the existence of Hopf bifur-cation are obtained by analyzing the associated characteristic equation.Furthermore,formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by center manifold theorem and normal form theorem of partial functional differential equations.