Mathematical analysis of a time-delayed model on brucellosis transmission with disease testing information
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.