关键词: 检测, 基本再生数, 后向分支, 一致持续, 最优控制

Abstract: Based on the fact  that infected animals found in animal detection still had  infectious characteristics, we established a dynamic model to analyze the influence of detection behavior on the spread of animal brucellosis. Firstly, the basic reproduction number of the model was given, and the existence of the equilibrium point was analyzed. Secondly, through the discussion of the equilibrium point, it was found that the model occured backward bifurcation. Lyapunov function was used to prove that when R₀<1, the equilibrium point of disease-free was globally asymptotically stable under certain condition, when R₀>1, the model was uniformly persistent. Thirdly,  the optimal control strategy was formulated and solved according to Pontryagin maximum principle. Finally,  the theoretical analysis results were validated by numerical simulation, indicating that the control strategy can effectively control the spread of animal brucellosis.

Key words: detection,  , basic reproduction number, backward bifurcation, uniformly persistent, optimal control