受疾病意识影响的时滞传染病模型的动力学分析

doi:10.13438/j.cnki.jdzk.2023.05.002

吉首大学学报（自然科学版） ›› 2023, Vol. 44 ›› Issue (5): 6-17.DOI: 10.13438/j.cnki.jdzk.2023.05.002

受疾病意识影响的时滞传染病模型的动力学分析

郭红利,谢景力,张美杨

(吉首大学数学与统计学院,湖南吉首 416000)

出版日期:2023-09-25 发布日期:2023-11-21
通讯作者: 谢景力(1972—),男,湖南辰溪人,吉首大学数学与统计学院教授,博士,主要从事微分方程与动力系统研究.
作者简介:郭红利(1999—),女,山西大同人,吉首大学数学与统计学院硕士研究生,主要从事微分方程与动力系统研究
基金资助:
湖南省教育厅科学研究重点项目（22A0368）；吉首大学研究生校级科研项目（JDY22005）

Dynamic Analysis of a Delayed Epidemic Model Affected by Disease Awareness

GUO Hongli,XIE Jingli,ZHANG Meiyang

(College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

Online:2023-09-25 Published:2023-11-21

摘要/Abstract

摘要：建立了一类受疾病意识影响且潜伏期具有时滞的SEIM传染病模型,给出了模型的基本再生数,并分析了模型的无病平衡点和地方病平衡点的存在性和稳定性.研究结果表明,当由潜伏期产生的时滞τ在相应的临界值τ₀处时,模型出现Hopf分支,2类平衡点的稳定性发生改变;当τ固定时,媒体报道力度越大,易感人群的疾病关注意识越强,感染者数量越少,疾病越容易得到控制.

关键词： 疾病意识, SEIM时滞模型, Hopf分支, 稳定性

Abstract: An SEIM delayed epidemic model affected by disease awareness and incubation period is established,the basic regeneration number of the model is given,and the existence and stability of the disease-free equilibrium point and the endemic equilibrium point of the model are analyzed.The results show that the Hopf bifurcation occurs in the model at the corresponding critical value τ₀ generated by the incubation period,and the stable state of the two equilibrium points changes.When τ is fixed,with the increase of media coverage,the stronger the awareness of disease among susceptible people and the smaller the number of infected people,the easier it is to control the disease.

Key words: disease awareness, delayed SEIM epidemic model, Hopf bifurcation, stability

郭红利, 谢景力, 张美杨. 受疾病意识影响的时滞传染病模型的动力学分析[J]. 吉首大学学报（自然科学版）, 2023, 44(5): 6-17.

GUO Hongli, XIE Jingli, ZHANG Meiyang. Dynamic Analysis of a Delayed Epidemic Model Affected by Disease Awareness[J]. Journal of Jishou University(Natural Sciences Edition), 2023, 44(5): 6-17.

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受疾病意识影响的时滞传染病模型的动力学分析

Dynamic Analysis of a Delayed Epidemic Model Affected by Disease Awareness

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