具有蚊子叮咬偏好性的扩散疟疾模型的动力学

杜彩虹

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

杜彩虹

西安电子科技大学数学与统计学院，西安 710126

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
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- 文章访问数: 556
- HTML全文浏览量: 189
- PDF下载量: 72
- 被引次数: 0
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

Dynamics of a Diffusion Malaria Model With Vector-Bias

DU Caihong

School of Mathematics and Statistics, Xidian University, Xi’an 710126, P.R.China

摘要

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
\begin{document}$ \mathcal{R}_0 $\end{document}
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。
- 疟疾模型 /
- 阈值动力学 /
- 季节性 /
- 蚊子叮咬的偏好性 /
- 空间异质性
Abstract:
In order to explore the combined effects of seasonality, vector-bias and human diffusion on malaria transmission, a partially degenerate periodic reaction-diffusion model was considered. With the persistence theory for dynamical systems, the threshold dynamics for the system was established in terms of basic reproduction number
\begin{document}$\mathcal{R}_0$\end{document}
. That is, the disease will go extinct if
$\mathcal{R}_0<1$
, while the disease will be uniformly persistent and break out seasonally for
$\mathcal{R}_0>1$
. Numerical results show that, the neglect of spatial heterogeneity and vector-bias will lead to underestimation of the risk of disease spread.
- malaria model /
- threshold dynamics /
- seasonality /
- vector-bias /
- spatial heterogeneity

HTML全文

图 1 $ {\cal{R}}_0>1 $ 时 $ I_{\rm{h}} $ 和 $ I_{\rm{m}} $ 的演化

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

下载: 全尺寸图片幻灯片

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 $

下载: 全尺寸图片幻灯片

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 $

下载: 全尺寸图片幻灯片

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

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

下载: 全尺寸图片幻灯片

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