Stability Analysis Of EB Virus Infection Dynamical Models

In this thesis,according to the infection principle of Epstein-Barr virus(EBV)to the host cells and the dynamic characteristics of EBV,we construct two dynamical models to analyze the characteristics of the disease.In the first chapter,we introduce the background of EBV,the progress of the study of dynamical models,the host anti EBV immune response and some basic mathematics theory.In the second chapter,we consider a dynamic model with bilinear infection function and the incubation period of delay.Firstly,we analyze the uniqueness,non-negativity,boundedness of the solution.Secondly,we take the disease-free equilibrium and the en-demic equilibrium point,then calculate the basic regeneration Ro.What's more,we prove the global stability of the two equilibrium points by constructing Lyapunov function and combining with the Lasalle invariable principles.In the end,we discuss the influence of parameters on the EBV infection,and analyzes how to effectively control parameters on the treatment of disease.In the third chapter,we establish a dynamic model considering virus infection and cell-to-cell infection.Firstly,we prove that the solution of the model is non-negative and bounded,and then calculate the basic regeneration R2.Secondly,we discuss the existence of the equilibria of the model.By constructing appropriate Lyapunov function,and combining with the Lasalle invariable principles,we establish the global stability of the disease-free equilibrium and the positive equilibrium.We discuss the influence of cell-to-cell parameters on the EBV infection in the end.In the last chapter,we make a brief review of the above conclusion,and present the practical meaning of these models.And we analyze some shortcomings of this thesis and point out some questions and future work.