吉林大学学报（理学版）2026，Vol.64Issue(3)：559-567,9.DOI:10.13413/j.cnki.jdxblxb.2025216
基于复杂网络的SEIR周期传染病传播模型的动力学分析
Dynamic Analysis of SEIR Periodic Infectious Disease Transmission Model Based on Complex Networks
摘要
Abstract
Based on the mean field theory of complex networks,we established a SEIR(susceptible,exposed,infectious,removed)model with periodic contagion rates.Firstly,we determined the positive invariant set of the system and used the spectral radius method of the linear integral operator to give the expression of the basic reproduction number R0.Secondly,by using the principle of comparison,we prove that the disease-free equilibrium point of the system is globally asymptotically stable when R0＜1,and there exists at least one positive periodic solution in the system and the system is uniformly persistent when Ro＞1.Finally,the correctness of the theoretical analysis is verified by using numerical simulations,and the results show that the greater the maximum degree of nodes in the network,the greater the absolute density of infected people,indicating that the network structure has a significant impact on the spread of infectious diseases.In addition,through numerical simulations,we obtain that when R0＞1,the system has a unique globally asymptotically stable positive periodic solution,which enriches the theoretical analysis results.关键词
周期性/基本再生数/正周期解/稳定性Key words
periodicity/basic reproduction number/positive periodic solution/stability分类
数理科学引用本文复制引用
杨佳,张瑞霞..基于复杂网络的SEIR周期传染病传播模型的动力学分析[J].吉林大学学报（理学版）,2026,64(3):559-567,9.基金项目
国家自然科学基金(批准号:12001501 （）
12071445 （）
11571324 （）
12101574)和山西省自然科学基金(批准号:20210302124621). （批准号:20210302124621）
