考虑媒体播报效应的双时滞传染病模型

廖书; 杨炜明

doi:10.21656/1000-0887.380025

考虑媒体播报效应的双时滞传染病模型

doi: 10.21656/1000-0887.380025

廖书,
杨炜明

重庆工商大学数学与统计学院, 重庆 400067

基金项目: 国家自然科学基金(11401059);重庆市科委基金(cstc2015jcyjA00024;cstc2015jcyjAX0067);重庆市教委科学技术研究项目(KJ1600610；KJ1706163)

详细信息

作者简介:
廖书(1980—), 女, 博士(通讯作者. E-mail: shuyang2011@yahoo.com);杨炜明(1981—), 男, 博士(E-mail: ywmctbu@gmail.com).

中图分类号: O175.13
计量
- 文章访问数: 1070
- HTML全文浏览量: 132
- PDF下载量: 714
- 被引次数: 0
出版历程
- 收稿日期: 2017-01-19
- 修回日期: 2017-04-23
- 刊出日期: 2017-12-15

An Epidemic Model With Dual Delays in View of Media Coverage

College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China

Funds: The National Natural Science Foundation of China(11401059)

摘要

摘要: 在疾病控制过程中, 媒体的重要性举足轻重.该文旨在建立并分析一个含有媒体效应的多时滞传染病模型, 研究模型的稳定性, 并通过分析相应特征方程根, 分别研究在时滞不同的5种情况下, 系统的稳定性发生变化, 以及产生Hopf分支的条件.再利用持续性理论, 证明模型的持续生存性.最后将时滞模型研究结果应用于苏格兰小儿肺炎中, 验证媒体效应对疫情控制起到的重要作用以及时滞大小对模型稳定性的影响.
- 媒体效应 /
- 传染病模型 /
- 多时滞 /
- 稳定性分析 /
- Hopf分支 /
- 持续性
Abstract: A multi-delay epidemic model in view of media coverage was established and analyzed. By means of the corresponding characteristic equation roots, the stability of the system was studied under 5 different time delay conditions, and the existence of the Hopf bifurcation was discussed. Furthermore, for a basic reproduction number greater than 1, the system’s uniform persistence was proved based on the persistence theory. At last, numerical simulations were conducted to verify the analytical predictions and evaluate the effects of media coverage and time delays on the control of emerging infectious diseases.
- media coverage /
- epidemic model /
- multiple delays /
- stability analysis /
- Hopf bifurcation /
- persistence

HTML全文

参考文献(20)

[1]	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):153-164.
[2]	Misra A K, Sharma A, Shukla J B. Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases[J]. Mathematical and Computer Modeling,2011,53(5/6): 1221-1228.
[3]	Cui J A, Sun Y H, Zhu H P. The impact of media on the control of infectious diseases[J]. Journal of Dynamics and Differential Equations,2007,20(1): 31-53.
[4]	Collinson S, Khan K, Heffernan J M. The effects of media reports on disease spread and important public health measurements[J]. PLoS ONE,2015,10(11): 1-21.
[5]	Misra A K, Sharma A, Singh V. Effect of awareness programs in controlling the prevalence of an epidemic with time delay[J]. Journal of Biological Systems,2011,19(2): 389-402.
[6]	刘玉英, 肖燕妮. 一类受媒体影响的传染病模型的研究[J]. 应用数学和力学, 2013,34(4): 399-407.( LIU Yu-ying, XIAO Yan-ni. An epidemic model with saturated media/psychological impact[J]. Applied Mathematics and Mechanics,2013,34(4): 399-407. (in Chinese))
[7]	Sun C, Yang W, Arinoa J, et al. Effect of media induced social distancing on disease transmission in a two patch setting[J]. Mathematical Biosciences,2011,230(2): 87-95.
[8]	张素霞, 周义仓. 考虑媒体作用的传染病模型的分析与控制[J]. 工程数学学报, 2013,30(3): 416-426.(ZHANG Su-xia, ZHOU Yi-cang. Analysis and control of an epidemic model with media influence[J]. Chinese Journal of Engineering Mathematics,2013,30(3): 416-426. (in Chinese))
[9]	Greenhalgh D, Rana S, Samanta S, et al. Awareness programs control infectious disease-multiple delay induced mathematical model[J]. Applied Mathematics and Computation,2015,251: 539-563.
[10]	Olowokure B, Odedere O, Elliot A J, et al. Volume of print media coverage and diagnostic testing for influenza A(H1N1)pdm09 virus during the early phase of the pandemic[J]. Journal of Clinical Virology,2012,55(1): 75-78.
[11]	Tchuenche J M, Bauch C T. Dynamics of an infectious disease where media coverage influences transmission[J]. ISRN Biomath,2012,2012(1). doi: 10.5402/2012/581274.
[12]	Funk S, Jansen V A. The talk of the town: modelling the spread of information and changes in behaviour[M]// Manfredi P, D’Onofrio A, ed. Modeling the Interplay Between Human Behavior and the Spread of Infectious Diseases.New York: Springer, 2012: 93-102.
[13]	Liu W. A SIRS epidemic model incorporating media coverage with random perturbation[J]. Abstract and Applied Analysis,2013,2013(2): 764-787.
[14]	Freedman H I, So J W H. Global stability and persistence of simple food chains[J]. Mathematical Biosciences,1985,76(1): 69-86.
[15]	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.
[16]	Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics [M]. Mathematics and Its Applications.Vol74. Dordrecht: Springer, 1992.
[17]	Hale J K. Theory of Functional Differential Equations [M]. Applied Mathematical Sciences. Vol3. New York: Spring-Verlag, 1977.
[18]	Hale J K, Waltman P. Persistence in infinite-dimensional system[J]. SIAM Journal on Mathematical Analysis,1989,20(2): 388-396.
[19]	Lamb K E, Greenhalgh D, Robertson C. A simple mathematical model for genetic effects in pneumococcal carriage and transmission[J]. Journal of Computational & Applied Mathematics,2011,235(7): 1812-1818.
[20]	Zhang Q, Arnaoutakis K, Murdoch C, et al. Mucosal immune responses to capsular pneumococcal polysaccharides in immunized preschool children and controls with similar nasal pneumococcal colonization rates[J]. Pediatric Infectious Disease Journal,2004,23(4): 307-313.