在媒体报道影响下具有隔离项的传染病模型的动力学分析
Dynamics of an SIQS Epidemic Model with Media Coverage
DOI: 10.12677/PM.2022.126115, PDF,    国家自然科学基金支持
作者: 张沐涵, 王思林, 王 琳：长春工业大学，吉林 长春
关键词: 媒体报道；隔离项；传染病模型；全局稳定性；Media Coverage； Quarantine； Infectious Disease Model； Global Stability
摘要: 本文采用分段光滑函数作为媒体影响函数引入到具有隔离项的SIQS传染病模型中，首先，得到平衡点的表达式，然后在R0 < 1和R0 > 1时分别分析平衡点的局部稳定性和全局稳定性。最后，利用数值模拟验证平衡点的全局稳定性并说明媒体报道和隔离策略的有效性。
Abstract: In this paper, the piecewise smooth function is used as the media influence function to SIQS infectious disease model. First, we get the expression of the equilibrium point, and then analyze the local stability and global stability of the equilibrium point respectively in R0 < 1 and R0 > 1. Finally, we use numerical simulation to verify the global stability of the equilibrium point and illustrate the effectiveness of media coverage and quarantine strategies.
文章引用：张沐涵, 王思林, 王琳. 在媒体报道影响下具有隔离项的传染病模型的动力学分析[J]. 理论数学, 2022, 12(6): 1047-1058. https://doi.org/10.12677/PM.2022.126115

参考文献

[1] 唐三一, 肖燕妮. 生物数学[M]. 北京: 科学出版社, 2019.
[2] 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]
[3] Hethcote, H., Ma, Z. and Liao, S. (2002) Effects of Quarantine in Six Endemic Models for Infectious Disease. Mathematical Biosciences, 180, 141-160. [Google Scholar] [CrossRef] 
[4] 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.
[5] King, S. and Striolo, A. (2021) An Engineering Model of the COVID-19 Trajectory to Predict the Success of Isolation Initiatives. UCL Open: Environment Preprint, 1-16. [Google Scholar] [CrossRef] 
[6] Cuello-Garcia, C., Perez-Gaxiola, G. and van Amelsvoort, L. (2020) Social Media Can Have an Impact on How We Manage and Investigate the COVID-19 Pandemic. Journal of Clinical Epidemiology, 127, 198-201. [Google Scholar] [CrossRef] [PubMed]
[7] Yang, A.J., Yuan, S.L. and Song, B.J. (2020) Noise-Induced Transitions in a Non-Smooth SIS Epidemic Model with Media Alert. Mathematical Biosciences and Engineering, 18, 745-763. [Google Scholar] [CrossRef] [PubMed]
[8] Wang, L.W., Zhou, D. and Liu, Z.J. (2017) Media Alert in an SIS Epidemic Model with Logistic Growth. Journal of Biological Dynamics, 11, 120-137. [Google Scholar] [CrossRef] [PubMed]
[9] Zu, J. and Wang, L. (2015) Periodic Solution for a Sea-sonally Forced SIR Model with Impact of Media Coverage. Advances in Difference Equations, 2015, Article No. 136. [Google Scholar] [CrossRef] 
[10] Liu, R. Wu, J. and Zhu, H.P. (2007) Media/Psychological Impact on Multiple Outbreaks of Emerging Infectious Diseases. Computational and Mathematical Methods in Medicine, 8, Article ID: 612372. [Google Scholar] [CrossRef] 
[11] Cui, J., Tao, X. and Zhu, H. (2008) An SIS Infection Model Incorporating Media Coverage. Journal of Mathematics, 38, 1323-1334. [Google Scholar] [CrossRef] 
[12] 刘玉英, 肖燕妮. 一类受媒体影响的传染病模型的研究[J]. 应用数学与力学, 2013, 34(4): 399-407.
[13] Wang, A.L. and Xiao, Y.N. (2014) A Filippov System Describing Me-dia Effects on the Spread of Infectious Diseases. Nonlinear Analysis: Hybrid Systems, 11, 84-97. [Google Scholar] [CrossRef] 
[14] Hale, J.K. (1980) Ordinary Differential Equations. Krieger Pub-lishing Company, Malabar.
[15] Odagaki, T. (2021) Exact Properties of SIQR Model for COVID-19. Physica A: Sta-tistical Mechanics and its Applications, 546, Article ID: 125564. [Google Scholar] [CrossRef] [PubMed]
[16] Corless, R.M., Gonnet, G.H. and Hare, D.E.G. (1996) On the Lambert W Function. Advances in Computational Mathematics, 5, 329-359. [Google Scholar] [CrossRef] 
[17] Li, M.Y. (2018) An Introduction to Mathematical Modeling of Infec-tious Diseases. Springer, Berlin. [Google Scholar] [CrossRef] 

为你推荐