Bifurcation analysis of a sheep brucellosis model with testing and saturated culling rate

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.