关键词: 传染性疾病, 乙型肝炎病毒, 免疫控制, 数学模型, 全局渐近稳定

Abstract: Tries to develop a mathematical model to express how the hepatitis B virus (HBV) spreads over and transforms from a state into other one by a set of differential equations. A conclusion can be drawn from it that if there is a positive equilibrium point found in the model, the disease elimination point is unstable and the infectious disease will spread over. It means that the disease or the model should be controlled effectively by way of immunization, i.e., isolating infants from their mothers and immunizing all infants. A Lyapunov function is therefore constructed and, according to the relevant theory of stability, it is proved that the model is globally stable at the disease elimination point after the immune control and, eventually, HBV will be eliminated. In addition, the conditions are obtained for extinction of HBV.