相邻场群上有迁移的动物疫病传播模型分析

Analysis of Animal Disease Transmission Model with Migration of Nearby Meadows

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.

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 mead- ows 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.