Dynamical Analysis Of Two HIV Models With C-M Incidence Rate And CTL Immune Response

In this paper, based on the process of HIV entrying into host cells and basic knowl-edge about HIV virus dynamics, we establish two mathematical models of HIV viral infection with C-M incidence rate and immune response. Then we study their dynamical behaviors.In the first chapter, we introduce the background of HIV virus infection,the devel-opment of viral dynamics and some relevant theoretical knowledge.In the second chapter, we establish an HIV virus model with C-M incidence rate and latent period.To describe the immune response effectively, we use a general im-mune rate. Then we compute the basic reproduction number and immune reproduction number. Besides, we analyze the existence of the virus free equilibrium,the immune-free equilibrium and immune equilibrium. By constructing Lyapunov functions, we establish the global stability of the virus-free equilibrium,immune-free equilibrium and immune equilibrium. At last,we discuss the recovery rate of infected cells in an eclipse stage.In the third chapter, considering immune response delay,we establish an HIV virus model with C-M incidence rate and immune response delay. By constructing Lyapunov functions,we establish the global stability of the disease-free equilibrium and immune-free equilibrium and discuss the existence of Hopf bifurcation. If there is no delays and the basic reproduction number R1>1, immune equilibrium is locally asymptotically stable.If the delay is greater than some critical value and the basic reproduction number R1>1, there is a Hopf bifurcation.In the last chapter,we make a brief review and discuss the biological and practical meaning of this paper.Then we analyze some shortcomings of this paper and put forward some future work.