Analysis Of Virus Dynamical Models With Cell-to-cell Viral Transmission

In this thesis, according to the infection process of HIV-1 virus to the host cells and the dynamic characteristics of HIV-1 virus, we propose a new form of infection incidence, and construct two dynamical models to analyze the characteristics of the disease.In the first chapter, we introduce the background of HIV-1, the progress of the study of dynamical models, the host anti HIV immune response, some basic mathematics theory and symbol description.In the second chapter, we construct a dynamic model considering virus infection and cell infection and with generally infection incidence rate kinetic model. Firstly, we prove the positivity and boundness of the model solution, and then calculate the basic reproduction number R0 of the model. Secondly, we discusses the existence and stability of the equilibria.In the third chapter, we establish a dynamic model considering virus infection and cell infection and with general infection incidence rate of continuous delay. Firstly, we prove that the solution of the model is positive and bounded, and then calculate the basic regeneration R0. Secondly, we discuss the existence of the equilibria of the model. By constructing appropriate Lyapunov functional, we establish the global stability of the disease-free equilibrium and the positive equilibrium.In the last chapter, we make a brief review of the above conclusion, and present the epidemic dynamic point of view and practical meaning for these models. And we analyze some shortcomings of this thesis and point out some questions and future work.