Dynamic Analysis On A Delayed HIV-1 Infection Model With Saturation Infection Rate

In this thesis, we study dynamics of a delayed HIV-1 infection model with sat-uration infection. Some su?cient conditions for its stability, permanence and Hopfbifurcation are established. The basic reproductive number R0 determining whetheror not the HIV-1 virus in host can be completely eliminated is obtained. If R0 < 1,then the infection-free equilibrium is stable. If R0 > 1, then the infected equilibriumappears and the virus infection is permanence.The thesis is composed of three chapters.In the first chapter, the historical background, signification and evolving of AIDSare brie?y reviewed. Furthermore, we simply introduce the main work in this paper.In the second chapter, considering the infection model with saturation infectionrate and discrete delay, we obtain two equilibria: infection-free equilibrium and infectedequilibrium. And we show the positivity and boundedness of the solutions to formulatethe well-posedness and the uniform permanence of the system.In the third chapter, stability of the infection-free equilibrium and the infectedequilibrium is studied. The su?cient conditions for the local and global stability of theinfection-free equilibrium are obtained. Criteria ensuring asymptotically stability of theinfected equilibrium for all delays are obtained. Choosing the delay as a parameter,we show that the existence of Hopf bifurcation at the infected equilibrium.In the fourth chapter, applying the normal form theory and center manifold ar-gument, we further study the direction and stability of Hopf bifurcation, deriving theexplicit formulae which determine the stability, the direction and the periodic of bifur-cating period solutions. Finally, we provide some numerical simulations to illustratethe analytical results obtained in this thesis.