基于继发性免疫失败的麻疹模型及其动力学行为

Dynamic Behaviors of a Measles Model Based on Secondary Vaccine Failure

建立一类基于接种疫苗引发的继发性免疫失败的麻疹传染病模型.先利用下一代矩阵法得到该模型的基本再生数R_(0),并给出其生物学意义;再通过构造合适的Lyapunov函数,证明R_(0)是一个阈值参数:当R_(0)≤1时,无病平衡点是全局渐近稳定的;当R_(0)>1时,无病平衡点是不稳定的,传染病平衡点是全局渐近稳定的.

We established a class of measles epidemic model based on secondary vaccine failure induced by vaccination.By using the next generation matrix method,we first obtained the basic reproduction number R 0 of the model and gave its biological meaning,and then proved that R 0 was a sharp threshold parameter by constructing an appropriate Laypunov function.When R_(0)≤1,the disease-free equilibrium is globally asymptotically stable;when R_(0)>1,the disease-free equilibrium is unstable and the endemic equilibrium is globally asymptotically stable.