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一类具时滞的周期logistic传染病模型空间动力学研究

王双明 张明军 樊馨蔓

王双明, 张明军, 樊馨蔓. 一类具时滞的周期logistic传染病模型空间动力学研究[J]. 应用数学和力学, 2018, 39(2): 226-238. doi: 10.21656/1000-0887.370301
引用本文: 王双明, 张明军, 樊馨蔓. 一类具时滞的周期logistic传染病模型空间动力学研究[J]. 应用数学和力学, 2018, 39(2): 226-238. doi: 10.21656/1000-0887.370301
WANG Shuangming, ZHANG Mingjun, FAN Xinman. Spatial Dynamics of Periodic ReactionDiffusion Epidemic Models With Delay and Logistic Growth[J]. Applied Mathematics and Mechanics, 2018, 39(2): 226-238. doi: 10.21656/1000-0887.370301
Citation: WANG Shuangming, ZHANG Mingjun, FAN Xinman. Spatial Dynamics of Periodic ReactionDiffusion Epidemic Models With Delay and Logistic Growth[J]. Applied Mathematics and Mechanics, 2018, 39(2): 226-238. doi: 10.21656/1000-0887.370301

一类具时滞的周期logistic传染病模型空间动力学研究

doi: 10.21656/1000-0887.370301
基金项目: 国家自然科学基金(61662066);甘肃科技计划(17JR5RA175);甘肃省高等学校科研项目(2017A-047)
详细信息
    作者简介:

    王双明(1987—),男,硕士(通讯作者. E-mail: wsm@lzufe.edu.cn);张明军(1973—),男,副教授,硕士(E-mail: zhangmjlz@163.com);樊馨蔓(1979—),女,副教授,硕士(E-mail: fanxm1120@163.com).

  • 中图分类号: O175

Spatial Dynamics of Periodic ReactionDiffusion Epidemic Models With Delay and Logistic Growth

Funds: The National Natural Science Foundation of China(61662066)
  • 摘要: 利用动力系统的理论研究一类具有时滞的周期logistic反应扩散传染病模型的动力学.首先证明了周期解半流对应ω算子的全局吸引子的存在性.然后利用次代算子方法引入了模型的基本再生数.最后,利用持久性理论结合比较原理,得到了疾病持久或灭绝的阈值条件:若基本再生数小于1,无病周期解是全局渐近稳定的,疾病将逐渐消失;若基本再生数大于1,系统一致持久,疾病将继续流行并最终形成地方病.
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出版历程
  • 收稿日期:  2016-09-30
  • 修回日期:  2017-12-21
  • 刊出日期:  2018-02-15

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