中北大学学报（自然科学版）2024，Vol.45Issue(4)：455-463,9.DOI:10.3969/j.issn.1673-3193.2024.04.006
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
摘要
Abstract
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 1 000 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 lag τ from 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 R0,β1 and γ1 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Key words
epidemic model/stability analysis/scale-free network/time delay/Hopf bifurcation分类
数理科学引用本文复制引用
王彤彤,刘茂省..带有时滞的SEAIQRS网络传染病模型动力学分析[J].中北大学学报（自然科学版）,2024,45(4):455-463,9.基金项目
国家自然科学基金资助项目(12071445,12001501) （12071445,12001501）
山西省自然科学基金资助项目(201901D211275) （201901D211275）
