乙型病毒性肝炎数学模型及其控制

针对乙型肝炎病毒的传播方式以及各种状态间的转化模式,建立由微分方程表达的乙型肝炎数学模型.分析表明,如果该模型有正平衡点,则疾病消除点不稳定,此时该传染病将会蔓延,因此应对疾病实施有效控制:在采取母婴阻断和新出生婴儿免疫控制方法的基础上,再对易感人群施加免疫控制.构造出一个Lyapunov函数,应用Lyapunov稳定性理论,证明了施加上述控制后,该传染病模型在疾病消除点全局渐近稳定,即乙肝病毒最终可以灭绝,并得出了乙肝病毒最终消除的免疫条件.

Mathematical Model of Hepatitis B and Its Control

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.