具有免疫时滞和综合干预措施的流感模型研究

An influenza transmission model with immune delay and comprehensive interventions

考虑了接种流感疫苗的个体具有确定的免疫期,建立了具有免疫时滞的SEIAR流感模型以探究“媒体、疫苗接种和抗病毒治疗”这三类综合干预措施对流感传播的影响.通过构造Lyapunov函数并依据Routh-Hurwitz判据,分析了模型的无病平衡点和地方病平衡点的稳定性,并给出了模型存在Hopf分支的充分条件.

In this paper,we consider that an individual with influenza vaccination has a defined immune period,so we establish an SEIAR influenza model with immune delay and three types of comprehensive interventions including"media,vaccination and antiviral therapy".By constructing the Lyapunov function and the Routh-Hurwitz criterion,the stability of the disease-free equilibrium and the endemic disease equilibrium of the model are analyzed.Furthermore,the sufficient condition for the existence of Hopf bifurcation near the endemic equilibrium is given out.