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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 ›› 2025, Vol. 42 ›› Issue (3): 439-454.doi: 10.3969/j.issn.1005-3085.2025.03.004doi: 32411.14.1005-3085.2025.03.004

• • 上一篇    下一篇

一类棘球蚴病传播模型的动力学分析

张  婧1,2,   胡卫敏1,3,   苏有慧2,   文  乾2   

  1. 1. 伊犁师范大学数学与统计学院，伊宁  835000
    2. 徐州工程学院数学与统计学院，徐州 221018
    3. 伊犁师范大学应用数学研究所，伊宁 835000
  • 收稿日期:2024-03-05 接受日期:2025-01-04 出版日期:2025-06-15 发布日期:2025-06-15
  • 通讯作者: 胡卫敏 E-mail: hwm680702@163.com
  • 基金资助:
    伊犁师范大学高级别培育项目 (YSPY2022014)；伊犁师范大学科研创新团队培育计划 (CXZK2021016)；新疆维吾尔自治区自然科学基金 (2023D01C51)；江苏省高等学校自然科学研究项目 (22KJB110026).

Dynamics Analysis of an Echinococcosis Transmission Model

ZHANG Jing1,2,   HU Weimin1,3,   SU Youhui2,   WEN Qian2   

  1. 1. School of Mathematics and Statistics, Yili Normal University, Yining 835000
    2. School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018
    3. Institute of Applied Mathematics, Yili Normal University, Yining 835000
  • Received:2024-03-05 Accepted:2025-01-04 Online:2025-06-15 Published:2025-06-15
  • Contact: W. Hu. E-mail address: hwm680702@163.com
  • Supported by:
    The High-level Cultivation Project of Yili Normal University (YSPY2022014); the Research and Innovation Team of Yili Normal University (CXZK2021016); the Natural Science Foundation of Xinjiang Uygur Autonomous Region (2023D01C51); the Natural Science Research Project of Jiangsu Colleges and Universities (22KJB110026).

摘要：

建立了棘球蚴病在牲畜、家犬、流浪狗及环境中虫卵的动力学模型，探讨了流浪狗在棘球蚴病传播中的影响。首先，利用微分方程基本定理得到了模型解的适定性，包括非负性和有界性。其次，得到了模型的平衡点和基本再生数，通过分析特征方程和Lyapunov函数构造得到：当基本再生数小于1时，无病平衡点全局渐近稳定，即棘球蚴病趋向灭绝；当基本再生数大于1时，无病平衡点不稳定，地方病平衡点全局渐近稳定，即棘球蚴病持续存在。

关键词: 棘球蚴病, 传染病动力学模型, 基本再生数, 全局渐近稳定性, 数值模拟

Abstract:

A dynamic model of echinococcosis in livestock, domestic dogs, stray dogs and eggs in the environment is established, and the influence of stray dogs on the transmission of echinococcosis is discussed. Firstly, by using the fundamental theorem of differential equation, the adaptability of the model solution is obtained, including non-negative and boundedness. Secondly, the equilibrium point and the basic regeneration number of the model are obtained. By analyzing the characteristic equation and the Lyapunov function, it is obtained that when the basic regeneration number is less than 1, the disease-free equilibrium point is asymptotically stable, namely, the echinococcosis tends to be extinct. When the basic regeneration number is greater than 1, the disease-free equilibrium point is unstable, and the endemic equilibrium point is asymptotically stable, namely, the echinococcosis persists.

Key words: echinococcosis, dynamic model of infectious diseases, basic regeneration number, global asymptotically stable, numerical simulations

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