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

作　　者：许云霞 雷学红 XU Yunxia;LEI Xuehong(School of Sciences,Kaili University,Kaili 556011,China)

机构地区：[1]凯里学院理学院,贵州凯里556011

出　　处：《湖北民族大学学报（自然科学版）》2020年第2期200-205,共6页Journal of Hubei Minzu University:Natural Science Edition

基　　金：贵州省教育厅青年科技人才成长项目(黔教合KY字[2019]186,黔教合KY字[2019]189);凯里学院校级课题(Z1706).

摘　　要：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.

关 键 词：哈密顿函数 传染病模型 全局稳定性 时滞 庞特里亚金极大值原理 

分 类 号：O175.1[理学—数学]