The Dynamics Analysis Of A Hepatitis B Virus Transmission Model

Hepatitis B is a potentially life-threatening liver infection caused by the hepati-tis B virus (HBV) and it is also a major global health problem. About 130 million people in China are carriers of HBV, almost a third of the people infected with HBV worldwide and about 10% of the general population in the country. In China, about 300,000 people die from HBV-related diseases every year, accounting for 40%-50% of HBV-related deaths worldwide. Despite an effective vaccination program for newborn babies has been settled since the 1990s, which has reduced chronic HBV infection in children, however, the incidence of hepatitis B is always increasing in China. This article uses a mathematical model to study the transmission dynamics and the prevalence of HBV infection in China.This article is divided into four chapters. In the first chapter we introduce the background of HBV, the epidemic of HBV in China and the current research status at home and abroad of the HBV models.The second chapter introduces the pre-knowledge, which concluds the defini-tions and the theorems, and the general method to calculate the basic reproductive number.In chapter three, We give some qualitative analysis of the model with slow and fast process. By using Routh-Hurwitz lemma,we get the local stability of the disease-free equilibrium. we apply the novel approach in Kamgang and Sallet(2008)to prove the conclusion that the disease-free equilibrium is globally asymptotically stable when the basic reproductive is less than unity. We discuss the existence and uniqueness of the positive equilibrium. By using the novel approach of convergence of trajectories within an invariant manifold in Rn, we study the global stability of endemic equilibrium. Finally, using MATLAB software to simulate the numbers of the model. In this paper, the results of numerical simulation consistent with the conclusion of the theorem we demonstrate, which well illustrates the correctness of the method. On the other hand, the structure of the model is reasonable.In chapter four, we summarize the current work and set the research targets.