Analysis Of HIV Infection Dynamic Models

In this paper, mathematical models are developed based on three medical facts about HIV infection. The dynamic properties with their biological meanings are studied. Background knowledge about HIV, progress of viral dynamics and some basic theory are introduced in Chap-ter1.A medical experiment published in Nature has shown that humanized mice receiving the vectored immunoprophylaxis can be fully protected from HIV infection. In Chapter2-a math-ematical model is proposed to investigate the viral dynamics under the effect of antibodies in the experiment. It is shown that the introduction of vectored immunoprophylaxis can induce the backward bifurcation and the ignorance of antibodies" loss due to their involvement with virus may result in the loss of backward bifurcation. By numerical simulations-it is found that the model also exhibits some other complicated dynamical behaviors. A subcritical Hopf bifurcation-a fold bifurcation of equilibria and a limit point bifurcation of limit cycles are de-tected, which induce five typical patterns of dynamical behaviors including the bistable phe-nomenon.A state of latent infection can be established in CD4+T cells and these latently infected cells are capable of abrogating CTL recognition. In Chapter3-a model with latent infection and CTL immune responses is developed based on this medical phenomenon. By constructing Lyapunov functions, the global stabilities of all the equilibria are obtained. It is also found that the ignorance of infection latency will lead to overestimate of reproduction numbers.The cell-to-cell transmission mode of HIV has aroused widespread concern in the medical world. In Chapter4, an elementary mathematical model is proposed to investigate the basic viral dynamics with cell-to-cell transmission. By constructing suitable Lyapunov functions, it is found that the dynamics of the model are completely determined by the basic reproduction number R0.When R0?1, the infection-free equilibrium is globally asymptotically stable and so is the infection equilibrium when R0>1.