一类脉冲免疫SIR传染病模型的无病τ周期解的存在性与稳定性  

Existence and Stability of Infection-free Periodic Solutions to Impulsively Vaccinating SIR Epidemic Model

作　　者：黄娜[1] 石志杰[1] 黄健民[1] 

机构地区：[1]广西师范大学,广西桂林541004

出　　处：《广西科学院学报》2011年第4期294-298,302,共6页Journal of Guangxi Academy of Sciences

基　　金：国家自然基金项目(10961005)资助

摘　　要：在脉冲免疫接种条件下,利用频闪映射的离散动力系统、Floquet乘子理论和脉冲微分方程比较定理,讨论一类具有阶段结构和Logistic死亡率的脉冲免疫接种SIR传染病模型,得到系统的无病τ周期解以及无病τ周期解的存在性和全局渐近稳定性的充分条件.An SIR epidemic model with generalized logistic death rate and stage structured was established.Using 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 illustrated.

关 键 词：脉冲方程 免疫接种 SIR模型 全局渐近稳定性 τ周期解 

分 类 号：O175[理学—数学]