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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 ›› 2015, Vol. 32 ›› Issue (6): 861-875.doi: 10.3969/j.issn.1005-3085.2015.06.007

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相邻场群上有迁移的动物疫病传播模型分析

樊洁茹1,   靳  祯1,2   

  1. 1- 中北大学理学院数学系，山西 太原 030051
    2- 山西大学复杂系统研究所，山西 太原 030006
  • 收稿日期:2014-03-28 接受日期:2015-01-12 出版日期:2015-12-15 发布日期:2016-02-15
  • 基金资助:
    国家自然科学基金 (11171314; 11331009).

Analysis of Animal Disease Transmission Model with Migration of Nearby Meadows

FAN Jie-ru1,   JIN Zhen1,2   

  1. 1- Department of Mathematics, Faculty of Science, North University of China, Taiyuan, Shanxi 030051
    2- Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006
  • Received:2014-03-28 Accepted:2015-01-12 Online:2015-12-15 Published:2016-02-15
  • Supported by:
    The National Natural Science Foundation of China (11171314; 11331009).

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摘要： 本文主要研究不同距离场群之间疫病的交叉感染和动物的迁移对动物疫病传播的影响．首先，根据疫病的传播基理，建立了相邻场群上有动物迁移的一类动物疫病传播模型．其次，利用微分方程定性稳定性理论，讨论了系统无病平衡点和地方病平衡点的存在性，证明了系统的无病平衡点是全局渐近稳定的．最后，对结果进行数值分析，定量分析了基本再生数对于不同参数的敏感性．结果表明，个体与环境细菌的接触传染系数以及个体从非相邻场群的迁入系数对基本再生数的影响较大．

关键词: 迁移, 基本再生数, 稳定性, 持续性

Abstract:

The paper mainly examines the influemce of cross-infection among meadows and animal migration on the spread of animal diseases. Firstly, based on mechanism of epidemic transition, an animal disease spreading model with animal migration among adjacent meadows is established. Then, applying the qualitative stability theory of differential equations, we discuss the existence of disease-free equilibrium and endemic equilibrium, proving that the disease-free equilibrium is globally asymptotically stable. Finally, numerical simulations are performed to verify the theoretical analysis results and the sensitivity of the basic reproduction number with respect to different parameters. The results indicate that the transmission coefficient of individuals contacting the bacteria around environment and the coefficient of individuals immigration from nonadjacent farms have signifiant influence on the basic reproduction number.

Key words: migration, basic reproduction number, stability, continuity

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