Dynamical Behaviors Of A Class Of HBV Infection Models

Dynamical models have played a more and more important role in the research of hepatitis B virus (HBV) infection. In this thesis, some significance biology findings are added to the basic model. An HBV infection model with Logistic hepatocyte growth, distributed delay and saturated CTL immune response and an HBV infection model with Logistic hepatocyte growth and cure rate are proposed and studied respectively. The biological meanings of the two models are discussed.In the first chapter, some biological background knowledge of HBV infection, the relevant progress in the research of HBV infection model and some basic mathematics theory are introduced.In chapter 2, dynamical behaviors of an HBV infection model with Logistic hepa-tocyte growth, distributed delay and saturated CTL immune response are studied. The model includes the ordinary differential equation, discrete delay differential equation and Gamma distributed delay differential equation models as three special cases. There al-ways exists two equilibria:the liver failure equilibrium which is unstable and the infection-free equilibrium which is globally asymptotically stable if the basic reproduction number R0≤1. There is an immune-free equilibrium if the basic reproduction number R0> 1 and an endemic equilibrium if the CTL immune response reproduction number R1> 1. The stability of these two equilibria in three models are studied respectively. In the ODE model, they are globally asymptotically stable under some conditions. However, there are Hopf bifurcations near the equilibria in the DDE model by using the delay as a bifurcation parameter. In the Gamma distributed delay model, numerical simulations have been done to find the Hopf bifurcations.In chapter 3, dynamical behaviors of an HBV infection model with Logistic hepa- tocyte growth and cure rate are studied. There always exists two equilibria:the liver failure equilibrium and the infection-free equilibrium. The sufficient conditions of the existence and uniqueness of the immune-free equilibrium and positive equilibrium are obtained. Two basic reproductive numbers:the basic reproduction number R0> 1 and the CTL immune response reproduction number R1> 1 are defined. The liver failure equilibrium is always unstable. By constructing Lyapunov function, the global stability of the infection-free equilibrium, immune-free equilibrium and the positive equilibrium are proved respectively.In the last chapter, the conclusions of this thesis are briefly reviewed and some disadvantages and future work are discussed.