一类受疾病意识和疫苗接种影响的时滞传染病模型  

A Delayed Epidemic Model Affected by Disease Awareness and Vaccination

作　　者：赵佳璐 谢景力[1] 汪雨琴 李嘉隆 ZHAO Jialu;XIE Jingli;WANG Yuqing;LI Jialong(College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

机构地区：[1]吉首大学数学与统计学院,湖南吉首416000

出　　处：《吉首大学学报(自然科学版)》2025年第2期10-22,共13页Journal of Jishou University(Natural Sciences Edition)

基　　金：湖南省教育厅科学研究重点项目(22A0368);吉首大学研究生科研创新项目(JDY2024071)。

摘　　要：建立了一类受疾病意识和疫苗接种影响的时滞传染病模型,给出了模型的基本再生数,分析了模型的无病平衡点和地方病平衡点的稳定性,给出了产生Hopf分支的判别条件,并讨论了疾病意识转化率和疫苗接种率对感染人群的影响.研究结果表明,当时滞为分支参数时,平衡点可能通过Hopf分支出现周期解.In this paper,a delayed epidemic model affected by disease awareness and vaccination is established.The basic regeneration number of the model is given,and the stability of the disease-free equilibrium point and the endemic equilibrium point of the model is analyzed.Then,the discriminant condition that generates Hopf bifurcation is provided,and the effects of disease awareness conversion rate and vaccination rate on infected population are studied.The results show that when the delay is the branch parameter,the equilibrium point may have periodic solutions through the Hopf bifurcation.

关 键 词：疾病意识 稳定性 时滞 HOPF分支 疫苗接种 

分 类 号：O175[理学—数学]