带有时滞的SEAIQRS网络传染病模型动力学分析  

Dynamic Analysis of SEAIQRS Network Epidemic Model with Time Delay

作　　者：王彤彤 刘茂省 WANG Tongtong;LIU Maoxing(School of Mathematics,North University of China,Taiyuan 030051,China;College of Science,Beijing University of Civil Engineering and Architecture,Beijing 102616,China)

机构地区：[1]中北大学数学学院,山西太原030051 [2]北京建筑大学理学院,北京102616

出　　处：《中北大学学报（自然科学版）》2024年第4期455-463,共9页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12071445,12001501);山西省自然科学基金资助项目(201901D211275)。

摘　　要：大多数经典的传染病模型并没有考虑到人口的异质性,为了更准确地描述新型冠状病毒的传播机制,考虑了基于无标度网络的带有时滞的SEAIQRS传染病模型。通过下一代矩阵法求得其基本再生数,并证明了正平衡点的存在唯一性,然后证明了模型在无病平衡点处Hopf分岔的存在性,最后利用MATLAB模拟了本文模型,通过在节点数为1000的无标度网络上运行30次取平均值得到关于各类人口的时间演化曲线,并利用PRCC敏感性分析研究了敏感性更强的参数对疾病传播的影响。结果表明,当R0>1时,疾病存在唯一正平衡点且是局部渐近稳定的,并且发现染病率和治愈率是影响疾病传播的关键参数。文中考虑了无症状染病者变为有症状染病者的时间滞后τ,这可能会导致传染病在传播过程中出现周期性传播的现象。为了达到控制传染病暴发的目的,通过数值模拟绘制了平面投影图来表明R_(0),β_(1)和γ_(1)三者之间的关系。In most classical epidemic models,the spatial heterogeneity of population is not considered.To describe the transmission mechanism of corona virus more appropriately,an SEAIQRS epidemic model with time delay based on scale-free network was established in this paper.The next-generation matrix method was used to calculate the basic reproduction number.Next,the uniqueness and the existence of the endemic equilibrium were demonstrated,and the existence of the Hopf bifurcation at the disease-free equilibrium was also proved.Finally,MATLAB was used to simulate the model of this paper.A scale-free network with 1000 nodes was averaged thirty times to obtain time evolution curves about each type of population,and the PRCC sensitivity analysis was performed to analyze the impact of more sensitive parameters on disease transmission.It is shown that when R0>1,the disease has a unique endemic equilibrium,which is locally asymptotically stable,and the infection rate and cure rate are the key parameters affecting the spread of the disease.The time lagτfrom asymptomatic infected people to symptomatic infected people is considered in this paper,which may lead to periodic transmission of diseases.Moreover,projection diagram planes are presented in the numerical simulation section to reflect the relationship between R_(0),β_(1)andγ_(1)in order to achieve the purpose of control the outbreaks.

关 键 词：传染病模型 稳定定性分析 无标度网络 时滞 HOPF分岔 

分 类 号：O175[理学—数学]