Analysis Of HBV Model With Humoral Immune Response And HBV DNA-containing Capsids

Hepatitis B virus(HBV)infection is one of the important research topics in the field of public health in the world.Since the humoral immune response and HBV DNA-containing capsids play an important role in the process of HBV infection and replica-tion,as well as,there are two different mechanisms of HBV infection in vivo:virus-cell infection and cell-cell infection,and it takes time for an antigen to stimulate the immune response,two kinds of HBV dynamical models with delays are established and analyzed in this thesis.The thesis includes four chapters.In Chapter 1,the biological background of Hepatitis B and the present situation at home and abroad of HBV dynamical models are briefly introduced,the main work and the theoretical basic knowledge of this thesis are summarized.In Chapter 2,an HBV infection model with humoral immune nonlytic and humoral immune delay is established and analyzed.Firstly,the positivity and boundedness of the solutions are proved,the basic reproduction number R₀is calculated and the existence of the equilibria is discussed.Secondly,local stabilities of the equilibria are proved,and the global stability of the disease-free equilibrium and the positive equilibrium without immune delay are proved by constructing Lyapunov functionals.At the same time,the existence of Hopf bifurcation for the system with immune delay is also discussed.Fi-nally,the above theoretical results are verified by numerical simulations,and the effects of nonlytic immune response on HBV infection are also investigated.In Chapter 3,an HBV infection model with HBV DNA-containing capsids,humoral immune delay and cell-cell infection is established and analyzed.Firstly,the positivi-ty and boundedness of the solutions are proved,and the existence of the equilibria is discussed by calculating the basic reproduction number R₀and immune response repro-duction number R₁.Secondly,by constructing Lyapunov functionals,global stabilities of the equilibria are proved.Thirdly,the effects of humoral immune delay on stability of the system are analyzed,the existence of Hopf bifurcation is discussed.Finally,the theoretical results are verified by numerical simulations and the influence of cell-cell infection on the model is analyzed.In the last chapter,the main work and conclusions are summarized,the shortcom-ings and further researches are discussed.