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具有蚊子叮咬偏好性的扩散疟疾模型的动力学

杜彩虹

杜彩虹. 具有蚊子叮咬偏好性的扩散疟疾模型的动力学 [J]. 应用数学和力学,2023,44(3):345-354 doi: 10.21656/1000-0887.430095
引用本文: 杜彩虹. 具有蚊子叮咬偏好性的扩散疟疾模型的动力学 [J]. 应用数学和力学,2023,44(3):345-354 doi: 10.21656/1000-0887.430095
DU Caihong. Dynamics of a Diffusion Malaria Model With Vector-Bias[J]. Applied Mathematics and Mechanics, 2023, 44(3): 345-354. doi: 10.21656/1000-0887.430095
Citation: DU Caihong. Dynamics of a Diffusion Malaria Model With Vector-Bias[J]. Applied Mathematics and Mechanics, 2023, 44(3): 345-354. doi: 10.21656/1000-0887.430095

具有蚊子叮咬偏好性的扩散疟疾模型的动力学

doi: 10.21656/1000-0887.430095
基金项目: 国家自然科学基金(11971369);中央高校基本科研业务费专项资金(JB210711)
详细信息
    作者简介:

    杜彩虹(1995—),女,硕士(E-mail:ducaihong0321@163.com)

  • 中图分类号: O29

Dynamics of a Diffusion Malaria Model With Vector-Bias

  • 摘要: 为了探讨季节性、蚊子叮咬的偏好性和人类的扩散对疟疾传播的影响,该文提出了一个部分退化的周期反应扩散模型。利用动力系统的持续性理论,研究了模型关于基本再生数 $ \mathcal{R}_0 $ 的阈值动力学。即当 $ \mathcal{R}_0<1 $ 时,疾病灭绝;而当 $ \mathcal{R}_0>1 $ 时,疾病一致持续,且会发生季节性的流行。数值上发现了忽略空间异质性和蚊子叮咬的偏好性会低估疾病传染的风险。
  • 图  1  $ {\cal{R}}_0>1 $$ I_{\rm{h}} $$ I_{\rm{m}} $ 的演化

    Figure  1.  The evolutions of $ I_{\rm{h}} $ and $ I_{\rm{m}} $ for $ {\cal{R}}_0>1 $

    图  2  蚊子叮咬的偏好性和人类的扩散对 $ {\cal{R}}_0 $ 的影响

    Figure  2.  The effects of vector-bias and human diffusion on $ {\cal{R}}_0 $

    图  3  季节性和空间异质性对 $ {\cal{R}}_0 $ 的影响

    Figure  3.  The effects of seasonality and spatial heterogeneity on $ {\cal{R}}_0 $

    图  4  $ {\cal{R}}_0 $$ D_{\rm{m}} $ 的变化

    Figure  4.  $ {\cal{R}}_0 $ as a function of $ D_{\rm{m }}$

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出版历程
  • 收稿日期:  2022-03-21
  • 修回日期:  2023-03-01
  • 网络出版日期:  2023-03-14
  • 刊出日期:  2023-03-15

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