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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 ›› 2023, Vol. 40 ›› Issue (4): 672-680.doi: 10.3969/j.issn.1005-3085.2023.04.012

• • 上一篇    

一类非线性传染病生态系统的泛函渐近解

徐建中1,  莫嘉琪2   

  1. 1. 亳州学院电子与信息工程系，亳州  236800;
    2. 安徽师范大学数学与统计学院，芜湖  241003
  • 收稿日期:2021-03-14 接受日期:2022-08-12 出版日期:2023-08-15 发布日期:2023-10-15
  • 基金资助:
    国家自然科学基金(11771005)；安徽省高校自然科学基金(KJ2019A1303; 2022AH052415)；安徽省2022年高校学科(专业)拔尖人才学术资助项目(gxbjZD2022080)；安徽省质量工程项目(2021jyxm0965).

A Class of Nonlinear Functional Asymptotic Solution of Ecological System of Contagious Diseases

XU Jianzhong1,  MO Jiaqi2   

  1. 1. Department of Electronics and Information Engineering, Bozhou University, Bozhou 236800;
    2. School of Mathematics & Statistics, Anhui Normal University, Wuhu 241003
  • Received:2021-03-14 Accepted:2022-08-12 Online:2023-08-15 Published:2023-10-15
  • Supported by:
    The National Natural Science Foundation of China (11771005); the key Natural Science Foundation of Universities  in Anhui Province (KJ2019A1303; 2022AH052415); the Program of Academic Funding for Top Talents of Higher Education Disciplines (Majors) in Anhui Province in 2022 (gxbjZD2022080); the Program for Quality Project in Anhui Province (2021jyxm0965).

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摘要：

讨论了一类非线性传染病传播群体的模型，利用泛函同伦映射的方法来探求传染病的传播规律，构造一对泛函同伦映照，讨论模型相应的线性系统。在一定的情况下，在零点处是一个稳定的结点，即原流行性传染病传播系统在零点处为稳定结点。因此，系统模型的时间当变量$t$趋于无穷时而趋于零点(解)。对于这种流行传染病传播模式，就能采取较好的措施，使传染病将得到控制。最后通过一个例子，说明了所用的方法的正确性，泛函同伦映照方法可采取对应的措施来控制它，解的表示式还能进一步进行解析运算。因此，它能够继续其它相关物理量的各种性态更深入的讨论。

关键词: 流行性传染病模型, 非线性方程, 动力系统

Abstract:

A nonlinear population model of an infectious disease transmission is proposed, and the method of functional homotopic mapping is used to explore the law of the infectious disease transmission. A pair of functional homotopic mappings is constructed and the corresponding linear system of the model is discussed. Under some circumstances, the zero point is a stable node, that is, the original epidemic transmission system is a stable node at zero point. Therefore, when the time variable $t$ of the system model tends to infinity, it tends to zero solution. Better measures can be taken to control the epidemic disease. Finally, an example illustrates the correctness of the method used. The functional homotopic mapping method can take corresponding measures to control it. The expression of the solution obtained can be further analyzed. It is therefore possible to continue further discussions of the various properties of other related physical quantities.

Key words: epidemic contagion model, nonlinear equation, dynamic system

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