Journal of Guangxi Normal University(Natural Science Edition) ›› 2026, Vol. 44 ›› Issue (2): 164-174.doi: 10.16088/j.issn.1001-6600.2025022503

• Mathematics and Statistics • Previous Articles     Next Articles

An Infectious Disease Model with Media Information and Imperfect Vaccination

LIU Shengqiang*, LIU Zehan, PIAN Xiaoyu   

  1. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
  • Received:2025-02-25 Revised:2025-05-28 Published:2026-02-03

PDF (PC)

1

Abstract: This paper investigates the impact of media coverage and imperfect vaccination on disease transmission by establishing an SIVR infectious disease model including an independent media information compartment M. The model analyzes the basic reproduction number, the stability of the disease-free equilibrium, the existence of the endemic equilibrium, and the conditions for backward bifurcation. The results indicate that the model exhibits complex dynamical behaviors, suggesting that media coverage and imperfect vaccination may increase the difficulty of disease control. Numerical simulations reveal bifurcation phenomena in the model, while also demonstrating that enhancing public awareness of media information and strengthening vaccination promotion can help reduce the number of infections. The study provides a theoretical foundation for understanding the role of media coverage and vaccination in disease transmission and offers references for formulating more effective public health strategies.

Key words: infectious disease, mathematical model, media information, vaccination rate, backward bifurcation

CLC Number:  O193
[1] 崔景安, 吕金隆, 郭松柏, 等.新发传染病动力学模型:应用于2019新冠肺炎传播分析[J].应用数学学报, 2020, 43(2):147-155.DOI:10.1360/SSM-2020-0026.
[2] RAI R K, TIWARI P K, KANG Y, et al.Modeling the effect of literacy and social media advertisements on the dynamics of infectious diseases[J].Mathematical Biosciences and Engineering, 2020, 17(5):5812-5848.DOI:10.3934/mbe.2020311.
[3] NIU Z M, QIN Z, HU P W, et al.Health beliefs, trust in media sources, health literacy, and preventive behaviors among high-risk Chinese for COVID-19[J].Health Communication, 2022, 37(8):1004-1012.DOI:10.1080/10410236.2021.1880684.
[4] LIU R S, WU J H, ZHU H P.Media/psychological impact on multiple outbreaks of emerging infectious diseases[J].Computational and Mathematical Methods in Medicine, 2007, 8(3):612372.DOI:10.1080/17486700701425870.
[5] LIU Y P, CUI J A.The impact of media coverage on the dynamics of infectious disease[J].International Journal of Biomathematics, 2008, 1(1):65-74.DOI:10.1142/s1793524508000023.
[6] LU X J, WANG S K, LIU S Q, et al.An SEI infection model incorporating media impact[J].Mathematical Biosciences and Engineering, 2017, 14(5/6):1317-1335.DOI:10.3934/mbe.2017068.
[7] WANG N, QI L X, BESSANE M, et al.Global Hopf bifurcation of a two-delay epidemic model with media coverage and asymptomatic infection[J].Journal of Differential Equations, 2023, 369:1-40.DOI:10.1016/j.jde.2023.05.036.
[8] XIE J L, GUO H L, ZHANG M Y.Dynamics of an SEIR model with media coverage mediated nonlinear infectious force[J].Mathematical Biosciences and Engineering, 2023, 20(8):14616-14633.DOI:10.3934/mbe.2023654.
[9] SONG P F, XIAO Y N.Analysis of a diffusive epidemic system with spatial heterogeneity and lag effect of media impact[J].Journal of Mathematical Biology, 2022, 85(2):17.DOI:10.1007/s00285-022-01780-w.
[10] LI T J, XIAO Y N.Complex dynamics of an epidemic model with saturated media coverage and recovery[J].Nonlinear Dynamics, 2022, 107(3):2995-3023.DOI:10.1007/s11071-021-07096-6.
[11] BUONOMO B, DELLA MARCA R.Oscillations and hysteresis in an epidemic model with information-dependent imperfect vaccination[J].Mathematics and Computers in Simulation, 2019, 162:97-114.DOI:10.1016/j.matcom.2019.01.005.
[12] 张真真, 李盈科, 赵睿轩.具有疫苗接种和年龄结构的疟疾传播模型的动力学行为[J].淮阴师范学院学报(自然科学版), 2024,23(4):288-296.DOI:10.16119/j.cnki.issn1671-6876.2024.04.012.
[13] 韩梦洁, 刘俊利.具有不完全接种的反应扩散禽流感模型[J].山东大学学报(理学版), 2023,58(10):106-121.
[14] MAHADHIKA C K, ALDILA D.A deterministic transmission model for analytics-driven optimization of COVID-19 post-pandemic vaccination and quarantine strategies[J].Mathematical Biosciences and Engineering, 2024, 21(4):4956-4988.DOI:10.3934/mbe.2024219.
[15] BUGALIA S, TRIPATHI J P, WANG H.Mutations make pandemics worse or better:modeling SARS-CoV-2 variants and imperfect vaccination[J].Journal of Mathematical Biology, 2024, 88(4):45.DOI:10.1007/s00285-024-02068-x.
[16] 王琪, 窦霁虹.一类考虑垂直传染、接种及人均病床数的SIVS传染病模型分析[J].西南师范大学学报(自然科学版), 2022, 47(10):26-36.DOI:10.13718/j.cnki.xsxb.2022.10.004.
[17] SAHA P, BISWAS S K, ALI BISWAS M H, et al.An SEQAIHR model to study COVID-19 transmission and optimal control strategies in Hong Kong, 2022[J].Nonlinear Dynamics, 2023, 111(7):6873-6893.DOI:10.1007/s11071-022-08181-0.
[18] LI Y, SAMREEN, ZADA L, et al.Assessing the impact of time-varying optimal vaccination and non-pharmaceutical interventions on the dynamics and control of COVID-19:a computational epidemic modeling approach[J].Mathematics, 2023, 11(20):4253.DOI:10.3390/math11204253.
[19] 黄自然, 古月明.一类肝吸虫病动力学模型及后向分支分析[J].赣南师范大学学报, 2024,45(6):9-13.DOI:10.13698/j.cnki.cn36-1346/c.2024.06.002.
[20] van den DRIESSCHE P, WATMOUGH J.Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J].Mathematical Biosciences, 2002, 180(1/2):29-48.DOI:10.1016/S0025-5564(02)00108-6.
[21] CASTILLO-CHAVEZ C, SONG B J.Dynamical models of tuberculosis and their applications[J].Mathematical Biosciences and Engineering, 2004, 1(2):361-404.DOI:10.3934/mbe.2004.1.361.
[1] ZHANG Wanjing, LIN Zhigui. Turing Instability of a Parasite-host Model on Growing Domains [J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(2): 132-139.
[2] FENG Jinming,LI Zunxian. Stability Analysis of a Class of Epidemic Model with Diffusion [J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(2): 63-68.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] TIAN Sheng, ZHAO Kailong, MIAO Jialin. Research on Automatic Driving Road Traffic Detection Algorithm Based on Improved YOLO11n Model[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(1): 1 -9 .
[2] XU Xiuhong, ZHANG Jinyan, LU Yuling, LIANG Xiaoping, LIAO Guangfeng, LU Rumei. Research Progress of New C21 Steroids in Medicinal Plants of Asclepiadaceae(Ⅱ)[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(2): 1 -16 .
[3] WANG Xingyu, ZHENG Haonan, LIU Xiao, CUI Shilong, CAI Jinjun. Research Progress on Preparation of Chitosan-based Adsorbents andTheir Applications Towards Adsorptive Removal of Pollutants From Water[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(2): 17 -30 .
[4] TIAN Sheng, FENG Shuaitao, LI Jia. A Framework for Enhanced Vehicle Trajectory Extraction in Urban Road Scenes[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(2): 31 -51 .
[5] LÜ Hui, SI Ke. Photovoltaic Panel Defect Detection Based on Improved RT-DETR[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(2): 52 -64 .
[6] SONG Guanwu, LI Jianjun. Semantic Segmentation of Remote Sensing Images Basedon Self-distillation Edge Refinement[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(2): 65 -76 .
[7] WANG Xuyang, LIANG Yuhang. Multi-scale Asymmetric Attention Transformer for Remote Sensing Image Dehazing[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(2): 77 -89 .
[8] ZHANG Shengwei, CAO Jie. Detection Algorithm of Tiny Defects on Steel Surface Based onFourier Convolution and Difference Perception[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(2): 90 -102 .
[9] WANG Wei, LI Zhiwei, ZHANG Zhaoyang, ZHANG Hong, ZHOU Li, WANG Zhen, HUANG Fang, WANG Can. Carbon Emission Prediction of Substation Based on IFA-BP Neural Network Model[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(2): 103 -114 .
[10] LUO Yuan, ZHU Wenzhong, WANG Wen, WU Yuhao. A Multi-step Water Quality Prediction Model Based on Improved PatchTST[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(2): 115 -131 .
Copyright © Journal of Guangxi Normal University(Natural Science Edition), All Rights Reserved.
Tel: 0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
Powered by Beijing Magtech Co. Ltd