一类具有两种控制策略的SIR非连续传染病模型动力学研究  

Dynamical Study on a Class of SIR Discontinuous Epidemic Model with two Control Strategies

作　　者：张仲华[1] 张靖茹 刘叶玲[1] ZHANG ZHONGHUA;ZHANG JINGRU;LIU YELING(School of Science,Xi’an University of Science and Technology,Shanxi 710054,China)

机构地区：[1]西安科技大学理学院,西安710054

出　　处：《应用数学学报》2020年第5期897-914,共18页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11201277);陕西省自然科学基金(2015JM011)资助项目。

摘　　要：本文分别以引起媒体预警的感染者数量及实施隔离措施的易感者数量为阈值,建立了一类具有两种控制策略的SIR传染病模型.采用Filippov凸组合等方法,系统地研究了具有两个正交不连续界面的微分方程系统在不同阈值条件下的动力学性质,如滑动区域,真、假平衡点的存在性,伪平衡点的存在性和稳定性及模型的全局渐近稳定性.最后,通过数值模拟验证所得结论.Considering the number of infected individuals warned by media and the number of susceptible individuals triggering isolation as two different thresholds,this paper formulates a kind of SIR epidemical model with two control strategies.The dynamic properties of differential equation system with two orthogonal discontinuous interfaces under different threshold conditions,such as the existence of sliding region,true and false equilibrium,the existence and stability of pseudo equilibrium and the global asymptotic stability of the model,are systematically studied by using Filippov convex combination method,etc.Finally,numerical simulations are carried out to support the conclusions.

关 键 词：传染病模型 滑模区域 稳定性 阈值策略 

分 类 号：O175.1[理学—数学]