Testing–culling is one of the important prevention and control measures considered in the study of animal infectious diseases. However, the process of finding infected animals (animal testing) is still not well studied through the kinetic model. In this paper, based on the characteristics of animal testing, a time-delayed model on brucellosis transmission is established. Under the general hypothesis of biological significance, the existence and stability of equilibria are first investigated. The results find that the global stability of equilibria depends on the basic reproduction number [Formula: see text] without the information delay: if [Formula: see text], the disease dies out; if [Formula: see text], the endemic equilibrium exists and the disease persists. Next, the impact of information delay on the dynamics of the model is analyzed and Hopf bifurcation is found in the established model when the information delay is greater than a critical value. Finally, the theoretical results are then further explained through numerical analysis and the significance of these results for the development of risk management measures is elaborated.

中文翻译：

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基于疾病检测信息的布鲁氏菌病传播延时模型的数学分析

检测-扑杀是动物传染病研究中考虑的重要防控措施之一。然而，发现感染动物的过程（动物测试）仍然没有通过动力学模型得到很好的研究。本文根据动物试验的特点，建立了布鲁氏菌病传播的延时模型。在生物学意义的一般假设下，首先研究了平衡的存在和稳定性。结果发现，平衡的全局稳定性取决于基本再生数[公式：见正文]，没有信息延迟：如果[公式：见正文]，则疾病消失；如果[公式：见正文]，地方病平衡存在，疾病持续存在。下一个，分析了信息延迟对模型动力学的影响，当信息延迟大于临界值时，建立的模型中发现了Hopf分岔。最后，通过数值分析进一步解释了理论结果，并阐述了这些结果对制定风险管理措施的意义。