Modeling And Simulating The Immune Response To The Hepatitis B Virus Infection

More than a third of the world's population has been infected with hepatitis B virus (HBV) and it is estimated conservatively that there are 350 million persistent carriers of HBV worldwide, 25% of whom have chronic liver disease and cirrhosis, which could progress to hepatocellular carcinoma. Chinese government expends about ten billions of yuan per annum and takes many measures to prevent and treat HB as China has the highest number of sufferers. The prevention and treatment of this infection is the present focus of the society and is the most important task in the medical fields.Animal tests and new techniques in molecular biology have been crucial in deepening our understanding of the pathogenetic mechanisms. Most of these new techniques have allowed the isolation of the process or cell under study so that the results can be readily interpretable. At the present time, however, there is an emerging need to understand the system in a whole, e.g. the immune system. Mathematical models can serve several distinct purposes. They can be used to analyze experimental results, to synthesize existing knowledge and provide a theoretical framework for the interpretation of existing paradigms so as to provide predictions and suggestions for follow-up experiments and treatment.The most common mathematical model in infection is presented by Nowak to explain the dynamics of host immune response to HIV and the pathogenesis of Aids. It is widely used to evaluate the antiviral effectiveness of drug treatment for HIV. The model is even used in the assessment of the efficiency of antiviral therapy for HBV and HCV. But it fails to explain the various outcomes of HBV infection.According to the principle of from simplicity to complexity, a simple model is established on the essential factors. When the model is proved to be able to simulate the various outcomes of HBV infection and the qualitative analysis results is in accordance with the clinical conclusion, more details are taken into account and more complex model is built the simpler model. The qualitative analysis results of the complex model should generalize the conclusion from the simple one. The values of the parameters in the simple model are used to reduce the workload of searching parameters for the complex model and the simulation results of the simple model is used as a criterion for judging the results of the complex one because of the absence of clinical data.Aimed at the shortcomings of Nowak's model, a modified cellular model is proposed. Using parameters evaluated by Nowak, the simulation results show that the new model can account for the wide variety of clinical manifestations of HBV infection. As the qualitative analysis result of this model is too complex to provide any useful information, the model is modified and the qualitative analysis result is simple and is in good agreement with the clinical results. As noncytolytic effects of CTL is found and proved to be more important than cytolytic effects in the clearance of infected cells, the model is rebuilt on this discovery and the qualitative analysis result is in accordance with the former result.The validation result of using clinical data demonstrates that the hepatocytes always die out. After analyzing the causation, hepatocyte proliferation function is regulated, and the equation is found considering the correlation between the functional defect of hepatocyte and clinical laboratory standard. A new model is constructed based on these. The model agrees with the clinical phenomenon that CHB infected with HAV hepatitis will always be completely cured, but the co-infection is easy to course fulminate hepatitis. The model simulates various results that appeared after HBV infection, and the delitescence, the aminotransferase and the HBV DNA concentration are all in the clinical range.On the basis of the former model, a new model of B-T cell co-operation including cellular immunity and humoral immunity is constructed. The results of qualitative analysis is in accordance with the conclusion above, and demonstrate the effect of humoral immunity in anti-infectious. The model using the former parameters and some new parameters could simulate various possible results after HBV infection. The simulated graphic is consistent with the trend graph promulgated by WHO.As APC plays a critical role in the immune reaction, a model considering APC, Helping T cells (Th1 and Th2), CTL, B cell and Ab is built based on the former model. The qualitative analysis result is the same as the former. The simulation results show that it can account for the wide variety of clinical manifestations.The parameters of a model that can simulate the outcome between the most serious one and recovery are enlarged to ten folds or zoom in 1/10 to show all the outcomes of HBV infection, and to analyze the influence of parameters on outcomes. The parameters favoring the immune system ate doubled and those favoring HBV are reduced to 1/2, so as it find out the most effective measures. The simulation results show that the most efficient measures change with different goals under different states. Treatment by blocking the denovo rate of infection or by reducing the production of visions is always the most efficient measure.