无标度网络上带有隔离项的时滞SIQRS模型稳定性分析  

Stability Analysis of Delayed SIQRS Model with Isolation Item on Scale-Free Networks

作　　者：徐云程 胡华 XU Yuncheng;HU Hua(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,Ningxia,China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《武汉大学学报（理学版）》2022年第3期324-334,共11页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金(11361044);宁夏自然科学基金(2021AAC03030);宁夏大学研究生创新项目(GIP2020060)。

摘　　要：考虑了无标度网络上一类带有隔离项的时滞SIQRS传染病模型的动力学行为。首先,利用地方病平衡态的存在性得到了基本再生数R_(0)的表达式;接着,通过构造适当的李雅普诺夫函数证明了平衡态的全局稳定性,结果表明:当R_(0)≤1时,无病平衡态全局渐近稳定,隔离措施对控制疾病传播没有影响;否则地方病平衡态全局渐近稳定,隔离措施在一定程度上降低了最终感染规模。最后,利用MATLAB软件对分析结果进行了数值模拟,发现当R_(0)<1时,时滞减缓了疾病的传播;当R_(0)>1时,时滞促进了疾病的传播。A scale-free network based SIQRS epidemic model with isolation item and time delay is considered in the present paper.At first,the formula of the basic reproduction number is given by utilizing the existence of the endemic equilibrium.Next,the global stability of the equilibrium is discussed by constructing appropriate Lyapunov functions,and the obtained results manifest that the disease-free equilibrium is globally asymptotically stable when R_(0)≤1,and isolate measures have no effect on controlling the spread of the disease.Otherwise the endemic equilibrium is globally asymptotically stable,and isolate measures reduce the final infection scale to a certain extent.Furthermore,the results are simulated by MATLAB.It is found that time delay slows down the spread of disease when R_(0)<1 and time delay promotes the spread of disease when R_(0)>1.

关 键 词：时滞 隔离措施 无标度网络 全局稳定性 

分 类 号：O211.63[理学—概率论与数理统计]