广西师范大学学报（自然科学版） ›› 2026, Vol. 44 ›› Issue (2): 164-174.doi: 10.16088/j.issn.1001-6600.2025022503

• 数学与统计学 • 上一篇    下一篇

具有媒体信息和不完善疫苗的传染病模型

刘胜强*, 刘泽含, 骈晓宇   

  1. 天津工业大学 数学科学学院,天津 300387
  • 收稿日期:2025-02-25 修回日期:2025-05-28 发布日期:2026-02-03
  • 通讯作者: 刘胜强(1975—),男,湖南宁乡人,天津工业大学教授,博导。E-mail: sqliu@tiangong.edu.cn
  • 基金资助:
    国家自然科学基金(12271401);天津市应用基础研究面上项目(22JCYBJC00080)

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

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摘要： 本文建立包含独立媒体信息仓室M的SIVR传染病模型,研究媒体报道和不完善疫苗接种对疾病传播的影响。模型分析了基本再生数、无病平衡点的稳定性、地方病平衡点的存在性及后向分支存在条件。结果表明,模型呈现复杂的动力学行为,表明媒体报道和不完善疫苗接种可能增加疾病控制的难度。数值模拟揭示了模型的分支现象,同时表明提高公众对媒体信息的认知、加强疫苗接种宣传有助于减少感染人数。本文研究为理解媒体报道和疫苗接种在疾病传播中的作用提供理论依据,并为制定公共卫生策略提供参考。

关键词: 传染病, 数学模型, 媒体信息, 疫苗接种, 后向分支

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

中图分类号:  O193

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