带有媒体报道影响的SEIQRM传染病模型的研究
Research on SEIQRM Infectious Disease Model Influenced by Media Reports
DOI: 10.12677/pm.2025.1510250, PDF,   
作者: 张沐涵：长春工业大学人文信息学院，数理教研部，吉林 长春；王 琳：长春理工大学，数学与统计学院，吉林 长春
关键词: 媒体报道；传染病模型；敏感性分析；基本再生数；Media Coverage； Epidemic Model； Sensitivity Analysis； The Basic Reproduction Number
摘要: 本文研究带有媒体报道影响的SEIQRM传染病模型，首先得到模型的基本再生数和平衡点，然后在 R 0 <1 和 R 0 >1 时分别分析平衡点的局部稳定性。最后用数值模拟说明媒体和隔离的有效性，并对模型进行敏感性分析。
Abstract: This article studies the SEIQRM infectious disease model with media coverage influence. Firstly, the basic reproduction number and equilibrium point of the model are obtained, and then the local stability of the equilibrium point is analyzed at R 0 <1 and R 0 >1 , respectively. Finally, numerical simulations are used to demonstrate the effectiveness of media and quarantine, and sensitivity analysis is conducted on the model.
文章引用：张沐涵, 王琳. 带有媒体报道影响的SEIQRM传染病模型的研究[J]. 理论数学, 2025, 15(10): 72-81. https://doi.org/10.12677/pm.2025.1510250

参考文献

[1] Tang, S. and Xiao, Y. (2007) One-Compartment Model with Michaelis-Menten Elimination Kinetics and Therapeutic Window: An Analytical Approach. Journal of Pharmacokinetics and Pharmacodynamics, 34, 807-827. [Google Scholar] [CrossRef] [PubMed]
[2] Li, M.Y. (2018) An Introduction to Mathematical Modeling of Infectious Diseases. Springer.
[3] 马知恩, 周义仓. 传染病动力学的数学建模与研究[M]. 北京: 科学出版社, 2014.
[4] Cui, J., Sun, Y. and Zhu, H. (2007) The Impact of Media on the Control of Infectious Diseases. Journal of Dynamics and Differential Equations, 20, 31-53. [Google Scholar] [CrossRef] [PubMed]
[5] Cui, J., Tao, X. and Zhu, H. (2008) An SIS Infection Model Incorporating Media Coverage. Rocky Mountain Journal of Mathematics, 38, 1323-1334. [Google Scholar] [CrossRef] 
[6] Zu, J. and Wang, L. (2015) Periodic Solutions for a Seasonally Forced SIR Model with Impact of Media Coverage. Advances in Difference Equations, 2015, Article No. 136. [Google Scholar] [CrossRef] 
[7] Lu, X., Wang, S., Liu, S. and Li, J. (2017) An SEI Infection Model Incorporating Media Impact. Mathematical Biosciences and Engineering, 14, 1317-1335. [Google Scholar] [CrossRef] [PubMed]
[8] Xie, J., Guo, H. and Zhang, M. (2023) Dynamics of an SEIR Model with Media Coverage Mediated Nonlinear Infectious Force. Mathematical Biosciences and Engineering, 20, 14616-14633. [Google Scholar] [CrossRef] [PubMed]
[9] Shi, X., Gao, X., Zhou, X. and Li, Y. (2021) Analysis of an SQEIAR Epidemic Model with Media Coverage and Asymptomatic Infection. AIMS Mathematics, 6, 12298-12320. [Google Scholar] [CrossRef] 
[10] Zhou, W., Xiao, Y. and Heffernan, J.M. (2019) Optimal Media Reporting Intensity on Mitigating Spread of an Emerging Infectious Disease. PLOS ONE, 14, e0213898. [Google Scholar] [CrossRef] [PubMed]
[11] Li, T. and Xiao, Y. (2022) Complex Dynamics of an Epidemic Model with Saturated Media Coverage and Recovery. Nonlinear Dynamics, 107, 2995-3023. [Google Scholar] [CrossRef] [PubMed]
[12] Qiu, H. and Hou, R. (2024) Dynamics and Optimal Control of an SEIAQR Epidemic Model with Media Coverage. Journal of Mathematical Analysis and Applications, 535, Article ID: 128192. [Google Scholar] [CrossRef] 
[13] Ma, Y., Liu, J. and Li, H. (2018) Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies. Mathematics, 6, Article 328. [Google Scholar] [CrossRef] 
[14] Deng, J., Tang, S. and Shu, H. (2021) Joint Impacts of Media, Vaccination and Treatment on an Epidemic Filippov Model with Application to Covid-19. Journal of Theoretical Biology, 523, Article ID: 110698. [Google Scholar] [CrossRef] [PubMed]
[15] Collinson, S., Khan, K. and Heffernan, J.M. (2015) The Effects of Media Reports on Disease Spread and Important Public Health Measurements. PLOS ONE, 10, e0141423. [Google Scholar] [CrossRef] [PubMed]
[16] Pan, J., Chen, Z., He, Y., Liu, T., Cheng, X., Xiao, J., et al. (2022) Why Controlling the Asymptomatic Infection Is Important: A Modelling Study with Stability and Sensitivity Analysis. Fractal and Fractional, 6, Article 197. [Google Scholar] [CrossRef] 

为你推荐