一类具有媒体影响因子和疫苗接种率的传染病模型

doi:10.13438/j.cnki.jdzk.2025.04.005

吉首大学学报（自然科学版） ›› 2025, Vol. 46 ›› Issue (4): 28-37.DOI: 10.13438/j.cnki.jdzk.2025.04.005

一类具有媒体影响因子和疫苗接种率的传染病模型

王立平,谢景力

(吉首大学数学与统计学院,湖南吉首 416000)

出版日期:2025-07-25 发布日期:2025-08-05
作者简介:王立平(1996—),男,湖南武冈人,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)

A Type of Infectious Disease Model with Media Impact Factor and Vaccination Rate

WANG Liping,XIE Jingli

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

Online:2025-07-25 Published:2025-08-05

摘要/Abstract

摘要：建立了一类具有媒体影响因子和疫苗接种率的传染病模型，利用下一代矩阵法给出了模型的基本再生数.通过构建Lyapunov函数并利用LaSalle不变原理,分析了模型的无病平衡点和地方病平衡点的存在性及稳定性.

关键词： 基本再生数, 媒体影响因子, 疫苗接种率, 有效传染率, 传染病模型

Abstract: A type of infectious disease model with media impact factor and vaccination rate has been established.The basic reproduction number of the model was given through the next-generation matrix method.Then,by constructing a Lyapunov function and utilizing the LaSalle invariance principle,the existence and stability of the disease-free equilibrium point and endemic equilibrium point of the model are analyzed.

Key words: basic regeneration number, media impact factor, vaccination rate, effective infection rate, epidemic model

王立平, 谢景力. 一类具有媒体影响因子和疫苗接种率的传染病模型[J]. 吉首大学学报（自然科学版）, 2025, 46(4): 28-37.

WANG Liping, XIE Jingli. A Type of Infectious Disease Model with Media Impact Factor and Vaccination Rate[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(4): 28-37.

参考文献

[1] LIU Yiping,CUI Jing'an.The Impact of Media Coverage on the Dynamics of Infectious Disease[J].International Journal of Biomathematics,2008(1):65-74.
[2] CUI Jing'an,TAO Xin,ZHU Huaiping.An SIS Infection Model Incorporating Media Convergence[J].The Rocky Mountain Journal of Mathematics,2008,38:1323-1334.
[3] FAHAD AL BASIR,SANTANU RAY,EZIO VENTURINO.Role of Media Coverage and Delay in Controlling Infectious Diseases:A Mathematical Model[J].Applied Mathematics and Computation,2018,337:372-385.
[4] SAMANTA SUDIP,RANA SOURAV,SHARMA ANUPAMA,et al.Effect of Awareness Programs by Media on the Epidemic Outbreaks:A Mathematical Model[J].Applied Mathematics and Computation,2013,219(12):6965-6977.
[5] SUN Chengjun,YANG Wei,ARINO JULIEN,et al.Effect of Media-Induced Social Distancing on Disease Transmission in a Two Patch Setting[J].Mathematical Biosciences,2011,230(2):87-95.
[6] 王晓娜,刘茂省,李有文.媒体报道对一类具有潜伏期的传染病控制的影响[J].数学的实践与认识,2012,42(23):173-178.
[7] ANNAS SUWARDI,PRATAMA MUH ISBAR,RIFANDI MUH,et al.Stability Analysis and Numerical Simulation of SEIR Model for Pandemic Covid-19 Spread in Indonesia[J].Chaos,Solitons & Fractals,2020,139:110072.DOI:10.1016/j.chaos.2020.110072.
[8] 邢伟,高晋芳,颜七笙,等.具有非线性传染率及脉冲免疫接种的SIQR传染病模型[J].广西师范大学学报(自然科学版),2017,35(2):58-65.
[9] DE LA SEN MANUEL,IBEAS ASIER,NISTAL RAUL.About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time Under Vaccination and Treatment Controls[J].Discrete Dynamics in Nature and Society,2021(1):1026-1226.
[10] SENAPATI ABHISHEK,RANA SOURAV,DAS TAMALENDU,et al.Impact of Intervention on the Spread of COVID-19 in India:A Model Based Study[J].Journal of Theoretical Biology,2021,523:110711.DOI:10.1016/j.jtbi.2021.110711.
[11] 刘中凯,刘俊利,刘白茹.受媒体报道和疫苗接种影响的传染病模型分析[J].哈尔滨商业大学学报(自然科学版),2022,38(4):442-449.
[12] BEACH BRIAN,CLAY KAREN,SAAVEDRA MARTIN.The 1918 Influenza Pandemic and Its Lessons for COVID-19[J].Journal of Economic Literature,2022,60(1):41-84.
[13] 孙雅楠,薛亚奎,孙松.受疾病意识影响的SIR传染病模型分析[J].华中师范大学学报(自然科学版),2021,55(3):337-342.
[14] 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.
[15] VAN DEN DRIESSCHE PAULINE V,WATMOUGH JAMES.Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission[J].Mathematical Biosciences,2002,180(1/2):29-48.

一类具有媒体影响因子和疫苗接种率的传染病模型

A Type of Infectious Disease Model with Media Impact Factor and Vaccination Rate

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