分数阶时滞传染病模型的传播动力学  

Propagation dynamics of fractional order delay epidemic model

作　　者：陈功 肖敏 万佑红[1] 王晓玲 CHEN Gong;XIAO Min;WAN You-hong;WANG Xiao-ling(College of Automation&College of Artificial Intelligence,Nanjing University of Posts and Telecommunications,Nanjing Jiangsu 210023,China)

机构地区：[1]南京邮电大学自动化学院人工智能学院,江苏南京210023

出　　处：《控制理论与应用》2021年第8期1257-1264,共8页Control Theory & Applications

基　　金：国家自然科学基金项目(62073172,61573194);江苏省自然科学基金项目(BK20181389);江苏省研究生科研和实践创新计划项目(SJCX200251)资助.

摘　　要：本文研究了一个具有时滞的分数阶SEIR传染病模型,并且着重研究了时滞的引入对模型的动力学行为的影响.首先,建立了分数阶SEIR传染病模型并给出了无时滞情况下地方病平衡点稳定的充分条件,以此来确保时滞的引入具有实际意义.其次,结合分岔理论求得了Hopf分岔发生的条件以及分岔阈值的表达式.研究发现,系统的动力学行为依赖于分岔的临界值.在此基础上,研究了分数阶阶次的变化对分岔阈值的影响,发现随着阶次的增加系统的Hopf分岔将会提前.最后用数值仿真结果来验证理论推导的正确性.In this paper,a fractional order SEIR epidemic model with time delay is investigated,and the effect of time delay on the dynamic behaviour of the model is investigated.Firstly,the fractional SEIR epidemic model is established and sufficient conditions for the stability of endemic equilibrium point without delay are given to ensure the practical significance of the introduction of time delay.Based on the bifurcation theory,the condition of the Hopf bifurcation and the expression of the bifurcation threshold are obtained.As it turns out,the dynamic behaviors of the system depend on the critical value of the bifurcation.On this basis,the influence of the fractional order on the bifurcation threshold is studied.It is found that the Hopf bifurcation of the system will advance as the order increases.Finally,the accuracy of the theoretical derivation is verified by numerical simulation results.

关 键 词：SEIR传染病模型 时滞 分数阶 HOPF分岔 

分 类 号：R181[医药卫生—流行病学] O175[医药卫生—公共卫生与预防医学]