一类具有Logistic死亡率的脉冲免疫接种SIRS传染病模型

摘要

An SIRS epidemic model with generalized Logistic death rate and standard incidence was formulated. By use of the discrete dynamical system determined by the stroboscopic map, an "infection-free" periodic solution of the model under impulsive vaccination was obtained. Based on Floquet theory and the comparison theorem of impulsive differential equation, the analysis of global asymptotic stability of the "infection-free" periodic solution was given. And the sufficient condition for the permanence of the system was obtained. The results show that in order to prevent the epidemic disease from generating an endemic, an appropriate vaccination rate and an appropriate vaccination period can be chosen.%建立了一类具有一般Logistic死亡率和标准传染率的SIRS传染病模型, 在脉冲免疫接种条件下, 利用离散动力系统的频闪映射方法, 得到了系统的无病周期解. 运用Floquet乘子理论和脉冲微分方程比较定理, 证明了该周期解的全局渐近稳定性, 并获得了系统一致持续生存的条件. 结果表明, 为了阻止疾病流行, 需要选择恰当的脉冲接种率和脉冲免疫接种周期.