Analysis Of Virus Dynamical Models With Cell-To-Cell Viral Transmission

In recent years, experimental studies have shown that virus (such as HTLV/HIV/HCV) can be transmitted directly from cell to cell by virological synapses and this way can resis-tant to neutralizing antibodies and lead to virus persistence. In this paper, we developed a class of virus dynamical models with cell-to-cell viral transmission. Two mathemati-cal models with cell-to-cell transmission and humoral immune response or discrete delay are studied respectively. The mathematical and biological meaning of each model is discussed.In Chapter 1, we introduce the progress of viral dynamics, background knowledge about cell-to-cell transmission and some basic theories involved in this paper.In Chapter 2, we present a class of virus dynamics model that including infection by free virus with general incidence rate and cell-to-cell transmission. Immune impairment is considered in the model because cell-to-cell transmission can evade antibody. We show that if the basic reproduction number R0< 1, the infection-free equilibrium is globally asymptotically stable by using the method of Lyapunov function. If Ro> 1, virus persists in the host. When there exits only one positive equilibrium, the antibodies persist. If the infected cells are greater than a threshold, the system has two positive equilibria. Bistability is shown to be possible and antibodies persist or die out depending on the initial status.In Chapter 3. we propose a virus dynamical model with cell-to-cell and discrete delay. We prove the positivity and boundedness of solutions and obtaine the reproductive number R0. If R0< 1, there always exits a infection-free equilibrium; if Ro> 1, endemic equilibrium exits. By constructing Lyapunov functional, we get the global stability of the infection-free equilibrium and endemic equilibrium.In the last chapter, we make a brief review of the above conclusions, and present the epidemic dynamic point of view and practical meaning for these models. And we analyze some shortcomings of this paper and point out some questions and future work.