具有Logistic增长的SIRS传染病模型的稳定性及最优控制分析

Dynamic Analysis and Optimal Control of an SIRS Epidemic Model with Logistic Growth

研究一类具有logistic增长的时滞SIRS传染病模型.证明了当基本再生数不大于1时,对于任意的时滞τ≥0,无病平衡点是全局渐近稳定的,此时疾病消亡.当基本再生数大于1时,得到了地方平衡点是全局渐近稳定的充分条件.利用控制理论,通过疫苗接种降低易感者和采取治疗措施提高感染者的恢复率来进行管理控制,利用Pontryagin最大值原理给出了最优控制策略对的表达形式.最后,通过MATLAB进行数值模拟,说明了采取最优控制对措施的有效性.

A delayed SIRS epidemic model with logistic growth was investigated.When the basic reproduction number was no more than one,we proved that the disease-free equilibrium was global asymptotically for the arbitrarily delayτ≥0,and disease died out.When it was greater than one,a sufficient condition for proving the global stability of the endemic equilibrium was derived.We used optimal control strategies in the form of vaccination and treatment to decrease the number of both susceptible and infectious individuals with minimum investment in disease control.The form of expression on the optimal controls was obtained.Finally,the numerical simulations results were presented to illustrate the effectiveness of the optimal controls by applying MATLAB.