基于检测行为的动物布病模型的动力学分析

Dynamic Analysis of Animal Brucellosis Model Based on Detection Behavior

基于动物检测中已发现的染病动物仍具有传染性的特点,建立动力学模型分析检测行为对动物布病传播的影响.首先,给出模型的基本再生数,并分析平衡点的存在性;其次,通过对平衡点的讨论发现模型会发生后向分支,用Lyapunov函数证明当R_(0)<1时,无病平衡点在一定条件下全局渐近稳定,当R_(0)>1时,模型是一致持续的;再次,根据Pontryagin极大值原理制定最优控制策略并进行求解;最后,通过数值模拟验证理论分析结果,表明控制策略可有效控制动物布病的传播.

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 R_(0)<1,the equilibrium point of disease-free was globally asymptotically stable under certain condition,when R_(0)>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.