Research On Hepatitis B Virus Models And Control Strategy Of HBV Infection

According to WHO's report, hepatitis B is a worldwide disease. Two billion people have been affected by hepatitis B virus and the number of chronic hepatitis B virus car-riers is up to 0.37 billion in the world. Because animal experimental cost for hepatitis B research is very high, theoretical analysis, quantitative analysis and simulation of mathemat-ical model should be applied to predict development of hepatitis B. Hepatitis B dynamics is an important theoretical analysis method to study hepatitis B development.In this paper, the establishment of HBV dynamical model and the control strategy of HBV are studied. Applying impulsive differential equation theorem to HBV dynamics, HBV model is established based on HBV characteristic and its dynamical characteristic is also analyzed. The research result can be used to predict development tendency of HBV infection. There are five chapters:Two types of hepatitis B models are established and studied in Chapter 2. Three types of hepatitis B model (spreading, time-delay, periodic inputting immune) are studied in Chapter 3.In Chapter four, HBV model involving time delay and diffusion phenomena is discussed. In the fifth chapter, the role of immune in HBV dynamics is discussed. The main work is as follows:Impulsive vaccination of hepatitis B is studied. The SAIR model with impulsive vac-cination is constructed. The sufficient conditions under which HBV would be eliminated ultimately or become endemic are derived. According to the propagation mode and the transformation mode between HBV infection states and the transformation delays, an HBV infection model with impulsive vaccination is established and analyzed. The sufficient con-ditions that hepatitis B virus will be eliminated eventually or be persistent are derived.The mutual effects of HBV, medicine and immune factors are studied. The HBV in-fection model considers diffusion within a finite domain and the time delay of cell infection and effect of medication. The effects of time delay and diffusion are validated by computer simulations. The research result is that the time delay and diffusion cannot affect HBV de-velopment. Usually only two time delays were considered in literature:disperse delays and continuous distributed delays. In the SIR model, continuous distributed delay is more inter-esting than disperse delay. Distributed delay is applied to HBV dynamics. The reciprocity model considering the mutual effects between uninfected cell, HBV, infected cell and im-munological factors with continuous distributed delays is established. The conditions for the disappearance or persistence of HBV, i.e., the global asymptotic stability or non-stability of the equilibrium points without disease, are derived. The effect of periodic input immune factor in HBV infection is also studied.The concurrent diffusion of HBV and medicine diffusion is studied. Based on the reaction diffusion system provided by Capasso and Maddalena, a delayed reaction-diffusion model is established to describe HBV infection and control. The sufficient conditions for the existence of traveling wave solutions of reaction-diffusion systems with delay are derived. The travelling wave front, derived here, corresponds to medicine injection that drives HBV to extinction. The parameter identification of interaction system between HBV and medicine with reaction-diffusion phenomenon is investigated.Under the condition of impulsive input medicine, the competition model between HBV and immune factor is studied. Population competitive Lotka-Volterra system is applied to explain the mutual effect of virus and immune factor. The prevention and control strategy derived is that periodic input medicine, shortening impulsive period can control HBV de-velopment. With limited liver area, logistic function is applied to formulate growth rate of healthy liver cell. Simulation shows that the input immune factor makes it stable. Differ-ent sets of parameters are used in the simulation, and the results show that the model can predict various clinical appearance of HBV infection. The simulation results suggest that a timely and vigorous CTL response is required in the treatment of HBV infection. No one considered the possible role of immune-dominance and vaccine in preventing and treating HBV infection in existing documents. In this part, we focus on aspects of the virus-specific cellular immune response, immune-dominance and influence of hepatitis B surface variant infection in vivo after vaccination. The stability conditions of the complete recovery equi-librium points at which HBV will be eliminated entirely from the body before and after vaccination are discussed. A different set of parameters is used in the simulation, and the results show that vaccination is an efficient way in preventing and treating HBV infection.As an application of dynamical control theorem to hepatitis B, the problem discussed here is of great importance. The results derived and methods applied provide important theoretical and practical value both in the study of HBV dynamical model and in the control of hepatitis B virus infection.