基于染病人数检测的布鲁氏菌病动力学模型分析

Analysis of Brucellosis Dynamics Model with the Number of Infected People as the Detection Information

以染病人数作为检测行为的依据,建立动力学模型来分析检测行为对布鲁氏菌病传播的影响.首先计算基本再生数R0,分析地方病平衡点的存在性;然后证明无病平衡点是全局渐近稳定的,当R0>1时疾病是一致持续的,并且得到了疾病的最优控制解;最后通过数值模拟发现,当参数满足一定条件时,系统会出现周期解.

The implementation of detecting and killing measures plays an important role in the prevention,control and purification of animal epidemic diseases.Considered the number of infected people as the basis of detection of behavior,a dynamic model has been established in this paper to analyze the impact of detection of behavior on the transmission of brucellosis.We first calculate the basic reproduction number of R0,and analyze the existence of endemic equilibrium point.Then it is proved that the disease-free equilibrium point is globally asymptotically stable,and the disease is uniformly persistent at R0>1 and the optimal control solution of the disease is obtained.Finally,it is found through numerical simulation that periodic solutions will appear when the parameters satisfy certain conditions.