Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2025, Vol. 42 ›› Issue (5): 935-948.doi: 10.3969/j.issn.1005-3085.2025.05.010

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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).

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

CLC Number: