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A Mathematical Model for Ovine Brucellosis during Dynamic Transportation of Sheep, and Its Applications in Jalaid Banner and Ulanhot City

Author

Listed:
  • Jiaming Guo

    (School of Mathematics, North University of China, Taiyuan 030051, China)

  • Xiaofeng Luo

    (School of Mathematics, North University of China, Taiyuan 030051, China)

  • Juan Zhang

    (Complex System Research Center, Shanxi University, Taiyuan 030006, China)

  • Mingtao Li

    (School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China)

Abstract

Brucellosis a the serious infectious disease in Hinggan League. Research has demonstrated that a large amount of transportation is one of the main reasons for so many cases. However, the specific transmission mechanism of brucellosis is not clear. In this paper, we utilize a multi-patch model to study the effect of the transportation of sheep on the spread of brucellosis in Hinggan League. Theoretically, we prove the global stability of the disease-free equilibrium and the uniform persistence of the endemic equilibrium. In a practical application, we apply the model to investigate the spread of brucellosis in Ulanhot city and Jalaid Banner, which are geographically adjacent in Hinggan League. The strains carried by humans are B.melitensis bv.1 and B.melitensis bv.3. We use the two-patch model to fit reported brucellosis cases data of two places by Markov Chain Monte Carlo (MCMC) simulations. It is found that the global basic reproduction number R 0 is larger than 1, but the isolated basic reproduction numbers in Ulanhot city and Jalaid Banner are both less than 1. This indicates that the prevalence of brucellosis may be caused by the transportation of sheep. Sensitivity analysis of parameters on R 0 shows that it is the most effective means to control the transportation of sheep from Jalaid to Ulanhot on preventing brucellosis. Moreover, we also discover that improving vaccine efficiency is an effective method compared with strengthening the vaccination coverage rate and improving the detection rate of sheep with brucellosis. Our dynamic behavior analysis of the two-patch model can provide a reference for the dynamic behavior analysis of the n -patch model, and our results provide a guide for how to control brucellosis based on transportation.

Suggested Citation

  • Jiaming Guo & Xiaofeng Luo & Juan Zhang & Mingtao Li, 2022. "A Mathematical Model for Ovine Brucellosis during Dynamic Transportation of Sheep, and Its Applications in Jalaid Banner and Ulanhot City," Mathematics, MDPI, vol. 10(19), pages 1-26, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3436-:d:921226
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    References listed on IDEAS

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    1. Liang, Juan & Liu, Chen & Sun, Gui-Quan & Li, Li & Zhang, Lai & Hou, Meiting & Wang, Hao & Wang, Zhen, 2022. "Nonlocal interactions between vegetation induce spatial patterning," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    2. Wei Zhang & Juan Zhang & Yong-Ping Wu & Li Li, 2019. "Dynamical Analysis of the SEIB Model for Brucellosis Transmission to the Dairy Cows with Immunological Threshold," Complexity, Hindawi, vol. 2019, pages 1-13, May.
    3. Luo, Xiao-Feng & Jin, Zhen & He, Daihai & Li, Li, 2021. "The impact of contact patterns of sexual networks on Zika virus spread: A case study in Costa Rica," Applied Mathematics and Computation, Elsevier, vol. 393(C).
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