Nie Yongbing, Sun Xiangdong, Hu Hongping, Hou Qiang
School of Mathematics, North University of China, Taiyuan, Shanxi 030051, China.
China Animal Health and Epidemiology Center, Qingdao, Shandong 266032, China.
Math Biosci Eng. 2023 Jan;20(1):1519-1537. doi: 10.3934/mbe.2023069. Epub 2022 Nov 3.
Testing-culling is a very effective measure for the prevention and control of animal diseases. In this paper, based on sheep brucellosis control policies and animal testing characteristics and considering the limitation of culling resources, a dynamic model is established to study the impact of testing-culling measure. Theoretical analysis reveals that the model may have one or three positive equilibria. The equilibrium in the middle is always unstable, and the model shows saddle-node bifurcation, generalized Hopf bifurcation and Bogdanov-Takens bifurcation. Moreover, the theoretical results are verified via numerical analysis. These results reveal that testing and culling strategies can induce complex transmission dynamics that can help us develop appropriate prevention and control measures for animal brucellosis.
检测扑杀是防控动物疾病的一项非常有效的措施。本文基于羊布鲁氏菌病防控政策和动物检测特点，考虑到扑杀资源的局限性，建立了一个动态模型来研究检测扑杀措施的影响。理论分析表明，该模型可能有一个或三个正平衡点。中间的平衡点总是不稳定的，并且该模型呈现出鞍结分岔、广义霍普夫分岔和博格达诺夫 - 塔克恩斯分岔。此外，通过数值分析验证了理论结果。这些结果表明，检测和扑杀策略可以诱导复杂的传播动态，这有助于我们制定针对动物布鲁氏菌病的适当防控措施。
