带时滞的羊-人传播的布鲁氏杆菌病模型的稳定性分析和最优控制

Stability Analysis of a Sheep-Human Transmitted Brucellosis Model with Time Delay

根据布鲁氏杆菌病高发地区的羊-人传播的特征,建立了具有时滞的布鲁氏杆菌病模型.根据下一代矩阵的方法得到了决定布鲁氏杆菌病流行和灭绝的阈值即基本再生数,并得出了模型的两个平衡点,通过LaSalle不变集原理和构造合适的Lyapunov函数证明了无病平衡点和地方病平衡点的全局渐近稳定性.进一步选择屠宰强度、免疫注射强度和宣传教育强度作为控制变量,制定了最优控制问题,得到了相应的最优控制策略.进行数值模拟验证了分析的结果,并对控制传染病的传播提出了合理的建议.

In this paper,we proposed a dynamical model with time-delay,according to the characteristics of sheep-human transmission in areas with high incidence of brucellosis.We used the next-generation matrix method to obtain the basic reproduction number of the model,which was the determinant of the prevalence and extinction of brucellosis.The local and global asymptotic stability of the two equilibria of the model was proved by LaSalle invariant set principle and the appropriate Lyapunov functions.Furthermore,slaughter intensity,immunization injection intensity and education intensity as the control variables,we obtained the optimal control strategy of the optimal problem.We put forward some reasonable suggestions for the spread and control of the disease and perform numerical simulation to verified the analysis results.