一类时滞分数阶SIR模型的动力学分析  

Dynamics Analysis of a Class of Fractional-order SIR Model with Time Delay

作　　者：张明月 肖敏 丁洁[1,2] 王璐[1,2] ZHANG Mingyue;XIAO Min;DING Jie;WANG Lu(College of Automation,Nanjing University of Posts and Telecommunications,Nanjing 210023,China;College of Artificial Intelligence,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]南京邮电大学自动化学院,江苏南京210023 [2]南京邮电大学人工智能学院,江苏南京210023

出　　处：《控制工程》2023年第10期1786-1792,共7页Control Engineering of China

基　　金：国家自然科学基金资助项目(62073172);国家自然科学基金资助项目(61573194);江苏省自然科学基金资助项目(BK20181389);江苏省研究生科研和实践创新计划项目(SJCX20_0251)。

摘　　要：为提高对传染病动力学模型分析的精确性,建立了一个新的带有时滞的分数阶传染病易感-感染-恢复(susceptible-infected-removed,SIR)模型,针对该模型进行稳定性分析并且讨论产生Hopf分岔的条件。首先,将整数阶系统转化为分数阶系统并求出正平衡点。然后,以时滞为分岔参数求出分岔点。研究发现,当时滞小于分岔点时,系统在正平衡点处是局部渐近稳定的;当时滞大于分岔点时,系统在正平衡点处发生Hopf分岔。同时,通过分析分数阶阶次对分岔点的影响发现,随着阶次的增加,系统的分岔点减小。最后,通过数值模拟验证了所得结论的准确性。In order to improve the accuracy of the analysis of the epidemic dynamics model,a new fractional-order epidemic susceptible-infected-removed(SIR)model with time delay is established,and the stability of the model is analyzed and the conditions for the Hopf bifurcation are discussed.Firstly,the integer-order system is converted to the fractional-order system,and the positive equilibrium point is obtained.Then,the time delay is used as the bifurcation parameter to find the bifurcation point.It is found that the system is locally asymptotically stable at the positive equilibrium point when the time delay is less than the bifurcation point.Hopf bifurcation occurs at the equilibrium point when the time delay is greater than the bifurcation point.At the same time,the influence of the fractional order on the bifurcation point is discussed,and it is found that the bifurcation point of the system decreases as the order increases.Finally,the accuracy of the conclusions is verified by numerical simulation.

关 键 词：传染病 稳定性分析 分数阶 时滞 HOPF分岔 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]