| 裴永珍,李长国,姬雪晖,陈兰荪.两类不同免疫策略下的SIR流行病模型[J].,2009,(3):459-462 |
| 两类不同免疫策略下的SIR流行病模型 |
| A SIR epidemic model with two different vaccination strategies |
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| DOI：10.7511/dllgxb200903028 |
| 中文关键词: 饱和传染力 连续免疫接种 脉冲免疫接种 全局稳定 一致持久 |
| 英文关键词: saturation infectious force continuous vaccination pulse vaccination global stability identical permanence |
| 基金项目:国家科技支撑计划资助项目(2008BAI68B01). |
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| 中文摘要: |
| 研究了两类不同免疫方式下具有饱和传染力的SIR流行病模型的动力学行为．在连续免疫接种方式下，确定了基本再生数 R 0 ．用Lassalle定理和Poincare-Bendixon的 三分法定理得到疾病消除平衡点和地方病平衡点全局渐近稳定的条件．在脉冲免疫接种方式下，确定了基本再生数 R ．利用脉冲微分方程的Floquet乘子理论和比较定理，研究了疾病消除周期解的全局渐近稳定性和系统的一致持久性．结果表明，当基本再生数小于1时，该传染病将逐渐消失；当基本再生数大于1时，该传染病将流行，成为地方病． |
| 英文摘要: |
| The dynamic behaviors of a kind of SIR epidemic model with two different vaccination strategies and saturation infectious force are researched. With continuous vaccination, the basic reproduction number R 0 is given. By Lassalle′s theorem and Poincare-Bendixon′s trichotomy theorem, the conditions of global asymptotic stability of disease-free equilibrium and endemic equilibrium are obtained. Moreover, with pulse vaccination, the basic reproduction number R is given. By using Floquet theory and comparison theorem of impulsive differential equation, the global asymptotic stability of the disease-free periodic solution and the identical permanence of system are researched. Results indicate that the disease will die out when the basic reproduction number is less than one, whereas the disease is persistent and becomes endemic when the basic reproduction number is more than one. |
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