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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 ›› 2025, Vol. 42 ›› Issue (5): 935-948.doi: 10.3969/j.issn.1005-3085.2025.05.010cstr: 32411.14.cjem.CN61-1269/O1.2025.05.010

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具有羊群输入的包虫病动力学建模与研究

贺艺玮,  崔倩倩   

  1. 宁夏大学数学统计学院,银川 750021
  • 收稿日期:2023-01-06 接受日期:2023-03-22 出版日期:2025-10-15 发布日期:2025-12-15
  • 通讯作者: 崔倩倩 E-mail: math_cui@126.com
  • 基金资助:
    国家自然科学基金 (12461100; 12001305).

Dynamics Modeling and Study of Echinococcosis with Sheep Input

HE Yiwei,  CUI Qianqian   

  1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021
  • Received:2023-01-06 Accepted:2023-03-22 Online:2025-10-15 Published:2025-12-15
  • Contact: Q. Cui. E-mail address: math_cui@126.com
  • Supported by:
    The National Natural Science Foundation of China (12461100; 12001305).

摘要:

建立了一类包虫病在犬–羊及环境中传播的动力学模型来探讨羊群输入对包虫病传播的影响。利用Lyapunov直接法和合作系统理论分析了模型的全局动力学行为。若没有感染羊群输入时,模型的动力学行为取决于基本再生数$R_0$,即当${{R}_{0}}<1$时,无病平衡点全局渐近稳定;而当${{R}_{0}}>1$时,地方病平衡点全局渐近稳定,疾病将持久存在。若有感染羊群输入时,理论上得到唯一的地方病平衡点是全局渐近稳定的,说明疾病将持久存在。数值仿真进一步探讨输入羊群对包虫病传播的影响,结果表明:当有羊群输入时,若有免疫羊群却无感染羊群将有利于当地包虫病的防控;若输入羊群含有感染羊群,则感染羊群的筛查成功率是影响包虫病传播的关键,筛查成功率越高,输入感染羊群越少,包虫病的流行程度越低。该结果为存在羊群输入地区的包虫病防控提供了一定的理论依据。

关键词: 传染病动力学模型, 包虫病, 羊群输入, 控制策略

Abstract:

A transmission dynamic model of echinococcosis among dogs, sheep and eggs was formulated to evaluate the effect of sheep input on the spread of echinococcosis. The global dynamic behavior of the model was analyzed by Lyapunov direct method and cooperative system theory.  Without the input of infected sheep, the dynamic behavior of the model depends on the basic reproduction number $R_0$, that is, when ${{R}_{0}}<1$, the disease-free equilibrium is global asymptotically stable, and when ${{R}_{0}}>1$, the endemic equilibrium is global asymptotically stable which means that the disease persists. With the input of infected sheep, the only endemic equilibrium theoretically is global asymptotically stable, indicating that the disease persists. The numerical simulation further discussed the influence of sheep input on transmission of echinococcosis. The results showed that when sheep are input, inputting immunized sheep but not infected sheep will be beneficial to local echinococcosis prevention and control. If infected sheep are input, the success rate of screening of infected sheep is the key factor affecting the transmission of echinococcosis. The higher the success rate of screening, the fewer infected sheep are input, and the lower the prevalence of echinococcosis. These results may provide technical supports for the prevention and control of echinococcosis in areas where sheep are input.

Key words: epidemic dynamical model, echinococcosis, sheep input, control strategy

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