具有饱和接触率与混合控制策略的SIQR模型的动力学分析  

Dynamic analysis of an SIQR model with saturation contact rate and hybrid strategies

作　　者：马艳丽[1] 褚正清[1] 李红菊[1] MA Yanli;CHU Zhengqing;LI Hongju(Department of Common Course, Anhui Xinhua University, Hefei 230088, China)

机构地区：[1]安徽新华学院通识教育部,安徽合肥230088

出　　处：《中国科学技术大学学报》2020年第5期682-687,共6页JUSTC

基　　金：安徽省高校自然科学重点研究项目(KJ2018A0598,KJ2019A0597,KJ2019A0875,KJ2019A0876);中国博士后科学基金(2017M621579);安徽新华学院自然科学重点研究项目(2019ZR005)资助.

摘　　要：考虑接种、隔离和剔除混合控制策略,建立了一个具有饱和接触率的SIQR传染病模型,从理论分析和数值模拟方面研究了该模型的全局稳定性.首先,通过计算得到了疾病灭绝与否的阈值—基本再生数R0和平衡点存在的条件;其次,当R0<1时,利用Liapunov函数证明了无病平衡点P0是全局渐近稳定的;然后,当R0>1时,运用Dulac函数证明了地方病平衡点P*是全局渐近稳定的;最后,利用计算机仿真,进一步证实理论分析的正确性.Considering vaccination,quarantine and elimination hybrid strategies,an SIQR epidemic model with saturation contact rate was established.And the global stability of the model was studied by means of both theoretical and numerical ways.Firstly,the threshold-basic reproductive number R0 which determines whether the disease is extinct or not and the conditions for the existence of equilibriums were obtained by the calculation.Secondly,by Liapunov function,it was proved that the disease-free equilibrium P0 is globally asymptotically stable when R0<1.Thirdly,by constructing a suitable Dulac function,it was obtained that the unique endemic equilibrium P*is globally asymptotically stable when R0>1.Finally,some numerical simulations were presented to illustrate the analysis results.

关 键 词：基本再生数 平衡点 全局渐近稳定性 LIAPUNOV函数 DULAC函数 

分 类 号：O175[理学—数学]