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Research on Hepatitis B Virus Models and Control Strategy of HBV Infection

Author: QiaoMeiHong
Tutor: QiHuan
School: Huazhong University of Science and Technology
Course: System Analysis and Integration
Keywords: Globally asymptotically stable The Persistence Time Delay Traveling wave solutions Reaction-diffusion equation Basic reproduction number
CLC: O242.1
Type: PhD thesis
Year: 2010
Downloads: 267
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Abstract


According to the World Health Organization, hepatitis B (HB) is a worldwide disease. More than 2 billion people worldwide have been infected with hepatitis B virus, chronic hepatitis B surface antigen as many as 370 million. Due to the high cost of hepatitis B to take the form of animal experiments, therefore, its pathogenesis, popular rule, forecasting more needs theoretical analysis, quantitative analysis, simulation, and the above analysis are from open mathematical model. Hepatitis B kinetics is popular law against hepatitis B, an important theoretical quantitative research methods. In this paper, kinetic models of hepatitis B and hepatitis B control strategy of the two major problems. Pulse theory of differential equations applied to the hepatitis B kinetics to establish a mathematical model of the dynamics of hepatitis B, according to the law of disease occurrence and spread in the population, and analysis of the kinetic properties of the model. The conclusions obtained can be used to predict changes in trends, find its prevention and control strategy, provides a theoretical basis for the development of prevention and treatment decision-making. The main work: pulse prevention of hepatitis B vaccination problem. Consider pulse SAIR hepatitis B vaccination model, respectively, to obtain a sufficient condition for hepatitis B eventually disappear or become endemic. Conversion mode according to the mode of transmission of the hepatitis B virus as well as a variety of state, each state into the desired time delay, pulse vaccination and other control measures take a class with delay and pulse vaccination SI1I2I3R hepatitis B model , respectively, to obtain a sufficient condition for hepatitis B eventually disappear or become endemic. The hepatitis B virus and drug interactions and immune factors the study of the problem. Consider the delay, the spread of the virus and the infected liver cells required to establish a class of spread of HBV in the limited area model, the impact of the delay and diffusion scenario simulation and verification. To the conclusion that the time delay and diffusion does not affect the development of the hepatitis B. Compartment model, distributed delay is more realistic than the discrete time delay. Will be distributed delays for hepatitis B kinetics, the disease-free equilibrium point globally asymptotically stable (HBV will disappear) and sufficient condition for instability (HBV persists). Finally, the study of the effect of the periodic input of immune factors in the treatment of HBV infection. The hepatitis B virus and drug proliferation issues at the same time. Reaction diffusion system based on the Capasso and Maddalena proposed, virus infection, hepatitis B virus and the mathematical model of drug interactions, the conditions for the existence of traveling wave solutions of the reaction-diffusion. Under these conditions, the existence of a hepatitis B virus from the existence of traveling wave solutions to the disappearance of the conditions for the persistence of hepatitis B virus in the liver. HBV and immune drug pulse factor competition model. Population competition Lotka-Volterra system to explain the interaction between the virus and immune factors, the proposed control measures: the periodic pulse injection drug reach the cycle to inhibit viral replication and proliferation rate appropriate to shorten the pulse period can control hepatitis B development. Consideration to the liver area is limited, the logistic function is applied as the growth rate of healthy liver cells, to create a class of hepatitis B model. The analysis and simulation results show that the the input immune factors can make the stability of the equilibrium point, and can predict a variety of clinical manifestations of HBV infection, timely and effective CTL response is very critical to the control of hepatitis B infection. There is no documentary evidence to consider the role of immune dominant and vaccines in the prevention and treatment of HBV infection. Concludes with a discussion of the effect of vaccination with surface antigenic variation of HBV infection, and to consider the impact of the virus-specific CTL response and HBV surface antigen variation before and after vaccination, has been before and after HBV vaccination is completely cleared from the body completely restore balance point stable conditions. Different set of parameters simulation showed that vaccination is an effective method of prevention of HBV infection. The problem studied in this paper is the dynamics control theory in the application on the hepatitis B, has great research value, belongs to the field of cutting-edge issues. The method used and the results obtained on the dynamic model of hepatitis B and control of hepatitis B virus infection has important theoretical and practical value.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Mathematical modeling, approximate calculation > Mathematical modeling
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