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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (1): 79-92.doi: 10.3969/j.issn.1005-3085.2022.01.006

• • 上一篇    下一篇

一类含多时滞和扩散项的非标准离散模型

廖  书,   方章英,   杨炜明   

  1. 重庆工商大学数学与统计学院，重庆 400067
  • 出版日期:2022-02-15 发布日期:2022-04-15
  • 基金资助:
    重庆市基础研究与前沿探索项目 (cstc2020jcyj-msxmX0394)；重庆市教委科学技术研究项目 (KJQN201900806)；经济社会应用统计重庆市重点实验室开放课题 (KFJJ2018067).

A Nonstandard Numerical Methods for a Mathematical Model for Cholera with Multiply Delays and Dispersal

LIAO Shu,   FANG Zhangying,   YANG Weiming   

  1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067
  • Online:2022-02-15 Published:2022-04-15
  • Supported by:
    The Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX0394); the Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJQN201900806); the Chongqing Key Laboratory of Social Economy and Applied Statistics (KFJJ2018067).

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摘要：

建立了一类以媒体效应作为主要预防传染病传播手段、并且含有多时滞和扩散项的传染病连续模型，并证明了该连续模型平衡点的全局稳定性。其次，利用非标准有限差分方法对该连续模型进行离散，离散后的模型具有和原连续模型一致的动力学性质。通过构造适当的李雅普诺夫函数，证明离散模型的平衡点在一定条件下也都是全局渐近稳定的。最后，数值模拟验证了理论结果。

关键词: 媒体效应, 反应扩散, 时滞, 非标准有限差分, 全局稳定

Abstract:

A spatial and delayed epidemic model with media coverage is studied, and the global asymptotically stability of the equilibria is proved. Furthermore, a discreted edition of this model is established by applying a nonstandard finite difference scheme which has the same dynamics as the original system. Moveover, it is shown that the global stability of the disease-free equilibrium, and the globally asymptotically stability of the endemic equilibrium is studied by constructing a suitable Lyapunov function. Finally, the NSFD scheme can be well simulated to support the theoretical results.

Key words: media coverage, reaction diffusion, delay, nonstandard finite difference scheme, global stability

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