1、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 wo

2、rld. Because animAlexperimentAlcost for hepatitis B
　　research is very high, theoreticAlanalysis, quantitative analysis and simulation of mathemat-
　　icAlmodel should be applied to predict development of hepatiti

3、s B. Hepatitis B dynamics is
　　an important theoreticAlanalysis method to study hepatitis B development.
　　 In this paper, the establishment of HBV dynamicAlmodel and the control strategy of
　　HBV are studied

4、. Applying impulsive differentiAlequation theorem to HBV dynamics,
　　HBV model is established based on HBV characteristic and its dynamicAlcharacteristic is
　　also analyzed. The research result can be used to pre

5、dict 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<

6、br>　　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. T

7、he 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
　　ul

8、timately 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 vaccinat

9、ion is established and analyzed. The sufficient con-
　　ditions that hepatitis B virus will be eliminated eventually or be persistent are derived.
　　 The mutuAleffects of HBV, medicine and immune factors are studi

10、ed. 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
　　

11、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 del

12、ays. 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 mutuAleffects between uninfec

13、ted cell, HBV, infected cell and im-
　　munologicAlfactors with continuous distributed delays is established. The conditions for the
　　disappearance or persistence of HBV, i.e., the globAlasymptotic stability or n

14、on-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

15、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

16、
　　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

17、 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

18、
　　and immune factor is studied. Population competitive Lotka-Volterra system is applied to
　　explain the mutuAleffect of virus and immune factor. The prevention and control strategy
　　derived is that periodi

19、c 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 inp

20、ut 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 clinicAlappearance of HBV infection. The simulation results

21、 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 infecti

22、on 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. T

23、he 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 i

24、n the simulation, and the
　　results show that vaccination is an ef?cient way in preventing and treating HBV infection.
　　 As an application of dynamicAlcontrol theorem to hepatitis B, the problem discussed