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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 ›› 2024, Vol. 41 ›› Issue (6): 1074-1086.doi: 10.3969/j.issn.1005-3085.2024.06.006

• • 上一篇    下一篇

具有季节性退化型反应扩散霍乱模型的动力学

褚慧洁   

  1. 西安电子科技大学数学与统计学院，西安 710126
  • 收稿日期:2022-04-07 接受日期:2022-06-21 出版日期:2024-12-15 发布日期:2024-12-15
  • 基金资助:
    国家自然科学基金 (11971369)；中央高校基本科研业务费 (JB210711).

Dynamics of a Degenerate Reaction-diffusion Cholera Model with Seasonality

CHU Huijie   

  1. School of Mathematics and Statistics, Xidian University, Xi'an 710126
  • Received:2022-04-07 Accepted:2022-06-21 Online:2024-12-15 Published:2024-12-15
  • Supported by:
    The National Natural Science Foundation of China (11971369); the Fundamental Research Funds for the Central Universities (JB210711).

摘要：

考虑霍乱的两种传播途径：人与人之间的直接传播和人与环境之间的间接传播，构建了一个部分退化的反应扩散方程模型，研究了季节性和人的活动对霍乱传播的影响。首先得到了解的存在唯一性、非负性、一致有界性和最终有界性。其次定义了模型的基本再生数，并证明了当基本再生数小于1时，疾病消除；当基本再生数大于1时，利用单调迭代方法确立了模型唯一正周期解的全局吸引性，表明了疾病的一致持续性。最后利用数值模拟探讨了模型关键参数对基本再生数的影响，结果表明空间异质性可能会降低疾病传播风险，而季节性因素并不总是有助于霍乱传播的。

关键词: 霍乱, 季节性, 扩散, 基本再生数, 阈值动力学

Abstract:

There are two transmission routes for cholera: the direct (human-to-human) and indirect (human-to-environment) transmission. Considering these two transmission mechanisms, a partially degenerate reaction-diffusion equation model is constructed to study the effects of seasonality and human activity on the spreading of cholera. First, we obtain the existence, un-iqueness and non-negativity of the solution and prove that the solution is ultimately uniformly bounded. Second, the basic reproduction number is identified, and it is shown that the disease will extinct when the basic reproduction number is less than 1. When the basic reproduction number is greater than 1, the global attractivity of the unique positive periodic solution is established using monotonic iteration method, which indicates that the disease will persist. Finally, we numerically explore the influences of key model parameters on the basic reproduction number. The results show that the spatial heterogeneity may reduce the risk of disease transmission, while the seasonal factors do not always contribute to the spread of cholera.

Key words: cholera, seasonality, diffusion, basic reproduction number, threshold dynamics

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