一类具有脉冲免疫的时滞SIRS传染病模型的全局分析

Global Analysis of a Delay SIRS Epidemic Disease Model with Pulse Vaccination

研究一类具有积分时滞的SIRS传染病动力学模型在脉冲免疫接种条件下的动力学行为.运用离散动力系统的频闪映射,获得一个"无病"周期解,证明该"无病"周期解是渐近稳定的.当模型的参数在适当条件下,该"无病"周期解是全局吸引的.运用脉冲时滞泛函微分方程理论获得带时滞系统持久性的充分条件,也得到该模型的全局吸引性条件.

An SIRS epidemic disease model with pulse vaccination and integral delays was considered,and dynamics behaiors of the model under pulse vaccination were analyzed. By use of the discrete dynamical system determined by the stroboscopic map,an ＂infection-free＂periodic solution was obtained and it iwas shown that the‘infection-free＇periodic solution was asymptotic stability. Then,it was proved that when some parameters of the model were in appropriate condictions,the ‘infection-free＇periodic sollution was globally attractive. Futher,with the theory on delay functional and impulsive differential equation,sufficient condiction with time delay for permanence of the system was given. At the same time,the condition of the global attractivity of the model was obtained.