| 一类具有治愈期和免疫失效期的SIRS模型 |
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| 引用本文： | 许立滨,李冬梅,杨美英.一类具有治愈期和免疫失效期的SIRS模型[J].哈尔滨理工大学学报,2014,19(6):113-117. |
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| 作者姓名： | 许立滨 李冬梅 杨美英 |
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| 作者单位： | 哈尔滨理工大学应用科学学院,黑龙江哈尔滨,150080 |
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| 基金项目： | 黑龙江省教育厅科学技术研究项目 |
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| 摘 要： | 考虑具有治愈期和免疫失效期的离散双时滞的SIRS传染病模型,找到决定疾病灭绝与否的阈值,计算出模型的无病平衡点和地方病平衡点,证明了无病平衡点的全局稳定性.并利用反证法和比较原理,证明疾病的一致持久性.并通过数值模拟分析治愈期和恢复期对模型的影响.
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| 关 键 词： | 双时滞 治愈期 免疫失效期 稳定性 一致持久性 |
The Stability and the Permanence of an SIRS Epidemic Model with Healing Period and Immune Expiration Period |
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| XU Li-bin,LI Dong-mei,YANG Mei-ying.The Stability and the Permanence of an SIRS Epidemic Model with Healing Period and Immune Expiration Period[J].Journal of Harbin University of Science and Technology,2014,19(6):113-117. |
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| Authors: | XU Li-bin LI Dong-mei YANG Mei-ying |
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| Affiliation: | (School of Applied Sciences, Harbin University of Science and Technology, Harbin 150080, China) |
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| Abstract: | An SIRS epidemic model with two time delays in healing period and immune expiration period is re- searched. The threshold conditions which determines the epidemic termination were found out, the free-equilibrium and endemic equilibrium were calculated, and the global stability of free-equilibrium was proved. Using the method of rebuttal evidence and the comparison principle of differential equations, the uniform persistence of disease is proved. Immune expiration period and the recover period for the influence of epidemic model by numerical simula- tion were analyzed at last. |
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| Keywords: | two time delays healing period immune expiration period stability uniform persistence |
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