| In this thesis, we investigate the dynamics of two HIV epidemic infection mod-els with immune response. Assume that there exists a time delay for immune re-sponse and the rate of the infection as well as the generation rate of uninfected cellsare general nonlinear functions, we establish the relevant mathematical models. Us-ing the basic theory of the diferential equation, we obtain the basic reproductivenumber0which determine whether or not the HIV virus in host can be com-pletely eliminated and1which determine the existence of CTLs response. Thethreshold value conditions ensuring the stability of the uninfected equilibrium, theinfected equilibrium without immune response and the infected equilibrium withimmune response are obtained.The paper is composed of three chapters.In the first chapter, the background, signification and evolving of epidemio-logical dynamics are briefly reviewed. Furthermore, we simply introduce the mainwork in this paper.In the second chapter, we consider a three-dimensional HIV infection modelwhich has the general nonlinear infection rate and immune delay. The basic re-productive number0for viral infection and1for CTLs response are obtained.By constructing Lyapunov functionals, it is shown that the uninfected equilibrium,the infected equilibrium without immune response and the infected equilibriumwith immune response are globally asymptotically stable in some threshold valueconditions.In the third chapter, considering the efect of viral load equation on the dynam-ics of system, assuming it has the saturation infection rate, we establish a delayedHIV infection model with Holling II type of infection function. We discuss the glob-al stability of three equilibriums by using the linearization equations, FluctuationLemma and Lasalle’s invariant principle, respectively. |
