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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (4): 60-71.doi: 10.6040/j.issn.1671-9352.0.2024.061

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复杂网络中带有自我防护意识的SEIR模型分析

秦佳欣,李淑萍*   

  1. 中北大学数学学院, 山西 太原 030051
  • 出版日期:2025-04-20 发布日期:2025-04-08
  • 通讯作者: 李淑萍(1979— ),女,副教授,硕士生导师,博士,研究方向为生物数学复杂网络. E-mail:lspnuc@126.com
  • 作者简介:秦佳欣(1999— ),女,硕士研究生,研究方向为生物数学复杂网络. E-mail:13007035925@163.com*通信作者:李淑萍(1979— ),女,副教授,硕士生导师,博士,研究方向为生物数学复杂网络. E-mail:lspnuc@126.com
  • 基金资助:
    国家自然科学基金资助项目(11701528,12101574,12001501);山西省自然科学基金资助项目(20210302124621,20210302123018)

Analysis of SEIR model with self-protection awareness in complex networks

QIN Jiaxin, LI Shuping*   

  1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
  • Online:2025-04-20 Published:2025-04-08

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摘要： 考虑媒体宣传和人与人之间的信息传播,在复杂网络上建立了具有2类易感仓室的易感者-暴露者-感染者-康复者(susceptible-exposed-infectious-removed, SEIR)模型,研究自我防护意识对于传染病传播的影响。得到了基本再生数R0,并且证明了当R0>1时,有唯一的地方病平衡点。根据Hurwitz判据和比较定理,分析了无病平衡点的稳定性,证明了当R0>1时,疾病是一致持续的。利用敏感性分析确定了参数对于R0的重要性。数值模拟表明,提高自我防护意识可以有效降低被感染的概率。

关键词: 自我防护意识, 复杂网络, 稳定性, 一致持续, 敏感性分析

Abstract: By considering media publicity and information dissemination among people, we establish an SEIR(susceptible-exposed-infectious-removed,)model with two types of susceptible compartments on complex networks to study the impact of self-protection awareness on the spread of infectious diseases. The basic reproduction number R0 is obtained by calculation, and it is proved that there is a unique endemic equilibrium point when R0>1. According to Hurwitz criterion and comparison theorem, the stability of the disease-free equilibrium is analyzed. Then it is proved that the disease is uniformly persistent when R0>1. Sensitivity analysis determines the importance of parameters for R0. Numerical simulation shows that improving self-protection awareness can effectively reduce the probability of being infected.

Key words: self-protection awareness, complex network, stability, uniform persistence, sensitivity analysis

中图分类号: 

  • O175
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