具有控制策略的媒介传染病模型的稳定性分析

Stability Analysis of Host-vector Epidemic Model with Control Strategy

主要研究了一类具有疫苗接种和媒介控制的媒介宿主传染病模型,采用下一代矩阵法得到了疾病流行与否的基本再生数的表达式,在系统存在平衡点的情况下,运用RouthHurwitz判据证明了两个平衡点局部渐近稳定,借助构造的Lyapunov函数,利用LaSalle不变原理以及第二加性复合矩阵等理论,证明了两个平衡点全局渐近稳定。理论结果表明当R_(0)<1时,疾病消失,无病平衡点全局渐近稳定;当R_(0)>1时,疾病持续逐渐形成地方病,唯一的地方病平衡点全局渐近稳定。

A kind of host-vector epidemic model with vaccination and vector control is studied.The basic reproduction number that determines whether the disease extinction or persistent is obtained by using the next generation matrix method and the existence of equilibrium point is analyzed,the local asymptotic stability of two equilibrium point are proved by Hurwitz criterion,the global asymptotic stability of two equilibrium points are proved by constructing suitable Lyapunov function,LaSalle invariant set principle and the second additive compound matrix.Results show that:when R_(0)<1,the disease disappears,with global asymptotic stability of disease-free equilibrium point;when R_(0)>1,the disease persists gradually and becomes endemic,with the global asymptotic stability of endemic equilibrium point.