SIRS传染病模型的连续接种和脉冲接种的比较  

Comparison between the continuous and pulse vaccinations about SIRS infectious disease model

作　　者：章培军[1] 李维德[2] 朱凌峰[2] 

机构地区：[1]西京学院基础部,西安710123 [2]兰州大学数学与统计学院,兰州730000

出　　处：《兰州大学学报（自然科学版）》2011年第1期82-86,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(40930533)

摘　　要：考虑了脉冲作用下的传染病模型,利用频闪映射及Floquet定理证明了具有脉冲接种且传染率为饱和的SIRS传染病模型的无病周期解的存在性,并多次利用比较原理和脉冲微分不等式证明了无病周期解的全局渐近稳定性.最后,对连续接种和脉冲接种作了比较,得出了相关的结论.A pulse under the action of infectious diseases model was considered. Using stroboscopic mapping and the Floquet＇s theorem, the existence of a disease-free periodic solution was proved concerning the SIRS epidemic model with pulse vaccination and a saturated infection rate. The global asymptotic stability of the disease-free periodic solution was also proved by using the comparison principle and pulse differential inequality. Finally, the continuous vaccination and pulse vaccination were compared and relevant conclusions were obtained.

关 键 词：脉冲微分方程 流行病模型 稳定性 基本再生数 

分 类 号：O175.13[理学—数学] Q141[理学—基础数学]