Dynamics Analysis Of HBV Diffusion Model With Acquired Immunity

Hepatitis B virus(HBV)infection is an important public health problem that seriously threatens human health.In the process of HBV infecting hepatocytes,immune response can lead to acute or chronic hepatitis,causing serious damage to the human liver.Therefore,it is particularly important to study the mechanism of HBV infection and how to reduce HBV infection.In this thesis,two kinds of dynamical models of HBV infection are established from the microscopic perspective for the interaction between immune response and virus.Precisely,we propose and study two such models as follows.In the first chapter,the damage of HBV infection,the infection process of HBV and the treatment of hepatitis B patients are briefly described.We also review the current status of the mathematical models for HBV and the related basic knowledge used in this dissertation.In the second chapter,considering the self-proliferation of healthy hepatocytes and two kinds of immune responses,we study the HBV infection diffusion model with Logistic growth and immune response.We show the positivity and boundedness of the model's solution and the existence of equilibrium points.We provide the threshold conditions for the existence of each equilibrium point.We also discuss the uniform persistence,local stability and global stability of the model.Lastly,the influence of immune response on the dynamics of HBV infection is evaluated by numerical simulations.In the third chapter,we study two infection modes of susceptible hepatocytes,namely direct infection by free virus particles and intercellular infection.We develop an HBV diffusion model with these two infection modes.We show the well-posedness of the model solution.We study the existence of five equilibria in this model,which are denoted by P₀,P₁,P₂,P₃and P₄.The global stability of each equilibrium of the model is proved.In the end,we illustrate the global stability of each equilibrium point via numerical simulations.