Mathematics and Computer Science |
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A delayed SIQR epidemic model with media effect and tracking quarantine |
Yuqian ZHANG(),Tailei ZHANG(),Wenshan HOU,Xueli SONG |
School of Science,Chang'an University,Xi'an 710064,China |
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Abstract In this paper, a delayed SIQR epidemic model with media effect and tracking quarantine is established, the basic reproduction number of the model is given. The model is analyzed theoretically and simulated numerically from the perspective of stability, persistence and bifurcation. The results show that Hopf bifurcations occur when the delay generated by media reports passes through a sequence of critical values. When is fixed, As the degree of deviation of susceptible persons' understanding of disease information under media reports increases continuously, the model will change from periodic oscillation to equilibrium point. With the increase of and , the maximum reduction effect of media reports on the effective contact rate, the model will change from equilibrium to periodic oscillation. Finally, the influence of different ,, and which denotes the accuracy of media reports on the relevant information of the quarantined persons on the development of infectious diseases is studied. The results suggest that it is beneficial for the media to widely report the information of infectious diseases and improve the information accuracy so as to reduce the spread of infectious diseases and effectively control the outbreak of infectious diseases.
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Received: 08 June 2021
Published: 22 March 2022
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Corresponding Authors:
Tailei ZHANG
E-mail: yuqianzhang2020@126.com;tlzhang@chd.edu.cn
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Cite this article:
Yuqian ZHANG,Tailei ZHANG,Wenshan HOU,Xueli SONG. A delayed SIQR epidemic model with media effect and tracking quarantine. Journal of Zhejiang University (Science Edition), 2022, 49(2): 159-169.
URL:
https://www.zjujournals.com/sci/EN/Y2022/V49/I2/159
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一类具有媒体效应和追踪隔离的SIQR时滞传染病模型
建立了一类具有媒体效应和追踪隔离的SIQR时滞传染病模型,给出了模型的基本再生数,并从稳定性、持久性和分支角度对该模型进行了理论分析和数值模拟。研究结果表明,由媒体报道产生的时滞在各影响因子的临界值处出现Hopf分支。当固定时,随着媒体的广泛报道,易感者对疾病信息认识的偏差程度不断增加,模型由周期性振荡转为平衡;随着有效接触率最大削减作用和的不断增加,模型又由平衡状态转为周期性振荡。还研究了,,以及被追踪隔离者相关信息的媒体报道准确率对传染病发展的影响。结果表明,媒体对传染病信息的广泛报道以及提高报道信息的准确率可降低疾病传播,有利于控制传染病。
关键词:
媒体报道,
追踪隔离,
SIQR时滞模型,
稳定性,
Hopf分支
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|
[1] |
唐三一,肖燕妮,梁菊花,等. 生物数学[M]. 北京:科学出版社, 2019. TANG S Y, XIAO Y N, LIANG J H, et al. Mathematical Biology[M]. Beijing: Science Press, 2019.
|
|
|
[2] |
邢伟,高晋芳,颜七笙,等. 一类受媒体报道影响的SEIS传染病模型的定性分析[J]. 西北大学学报(自然科学版),2018,48(5): 639-643. doi:10.16152/j.cnki.xdxbzr.2018-03-003 XING W, GAO J F, YAN Q S, et al. An epidemic model with saturated media/psychological impact[J]. Journal of Northwest University(Natural Science Edition), 2018, 48(5): 639-643. doi:10.16152/j.cnki.xdxbzr.2018-03-003
doi: 10.16152/j.cnki.xdxbzr.2018-03-003
|
|
|
[3] |
赵晓艳,明艳,李学志. 一类考虑媒体报道影响的传染病模型分析[J]. 数学的实践与认识,2018, 48(10): 314-320. ZHAO X Y, MING Y, LI X Z. Analysis of a kind of epidemic model with the impact of media coverage[J]. Journal of Mathematics in Practice and Theory, 2018, 48(10): 314-320.
|
|
|
[4] |
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. doi:10.3879/j.issn.1000-0887.2013.04.008 LIU Y Y, XIAO Y N. An epidemic model with saturated media / psychological impact[J]. Applied Mathematics and Mechanics, 2013, 34(4): 399-407. doi:10.3879/j.issn.1000-0887.2013.04.008
doi: 10.3879/j.issn.1000-0887.2013.04.008
|
|
|
[5] |
ZHANG Y D, HUO H F, XIANG H. Dynamics of tuberculosis with fast and slow progression and media coverage[J]. Mathematical Biosciences and Engineering, 2019, 16(3): 1150-1170. doi:10.3934/mbe.2019055
doi: 10.3934/mbe.2019055
|
|
|
[6] |
CHANG X H, LIU M X JIN Z, et al. Studying on the impact of media coverage on the spread of COVID-19 in Hubei province, China[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3147-3159. doi:10.3934/mbe.2020178
doi: 10.3934/mbe.2020178
|
|
|
[7] |
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, 2008, 20: 31-53. doi:10.1007/s10884-007-9075-0
doi: 10.1007/s10884-007-9075-0
|
|
|
[8] |
LI Y F, CUI J A. The effect of constant and pulse vaccination on SIS epidemic models incorporation media coverage[J]. Communications in Nonlinear Science and Numerical Simulation, 2008, 14(5): 2353-2365. doi:10.1016/j.cnsns.2008.06.024
doi: 10.1016/j.cnsns.2008.06.024
|
|
|
[9] |
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. doi:10.1080/17486700701425870
doi: 10.1080/17486700701425870
|
|
|
[10] |
TCHUENCHE J M, BAUCH C T. Dynamics of an infectious disease where media coverage influences transmission[J]. ISRN Biomathematics, 2012, 2012:581274. doi:10.5402/2012/581274
doi: 10.5402/2012/581274
|
|
|
[11] |
XIAO Y N, ZHAO T T, TANG S Y. Dynamic of an infectious diseases with media psycholology induced non-smooth incidence [J]. Mathematical Biosciences and Engineering, 2013, 10(2): 445-461. doi:10.3934/mbe.2013.10.445
doi: 10.3934/mbe.2013.10.445
|
|
|
[12] |
XIAO Y N, TANG S Y, WU J H. Media impact switching surface during an infectious disease outbreak[J]. Scientific Reports, 2015, 5: 7838. doi:10.1038/srep07838
doi: 10.1038/srep07838
|
|
|
[13] |
YAN Q L, TANG S Y, WU J H, et al. Media coverage and hospital notifications: Correlation analysis and optimal media impact duration to manage a pandemic[J]. Journal of Theoretical Biology, 2016, 390: 1-13. doi:10.1016/j.jtbi.2015.11.002
doi: 10.1016/j.jtbi.2015.11.002
|
|
|
[14] |
YAN Q L, TANG S Y, YAN D D, et al. Impact of media reports on the early spread of COVID-19 epidemic[J]. Journal of Theoretical Biology, 2020, 502: 110385. doi:10.1016/j.jtbi.2020.110385
doi: 10.1016/j.jtbi.2020.110385
|
|
|
[15] |
李芳,刘茂省. 具有媒体饱和效应影响的时滞SIS模型研究[J]. 数学的实践与认识, 2017,47(10): 215-221. LI F, LIU M X. A class of delay SIS model with media saturation [J]. Journal of Mathematics in Practice and Theory, 2017, 47(10): 215-221.
|
|
|
[16] |
AI BASIR F, SANTANU R, EZIO V. Role of media coverage and delay in controlling infectious diseases: A mathematical model[J]. Applied Mathematics and Computation, 2018, 337(15): 372-385. doi:10.1016/j.amc.2018.05.042
doi: 10.1016/j.amc.2018.05.042
|
|
|
[17] |
AGABA G O, KYRYCHKO Y N, BLYUSS K B. Dynamics of vaccination in a time-delayed epidemic model with awareness[J]. Mathematical Biosciences, 2017, 294:92-99. doi:10.1016/j.mbs.2017.09.007
doi: 10.1016/j.mbs.2017.09.007
|
|
|
[18] |
SHI L, ZHAO H Y, WU D Y. Modelling and analysis of HFMD with the effects of vaccination, contaminated environments and quarantine in mainland China[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 474-500. doi:10.3934/mbe.2019022
doi: 10.3934/mbe.2019022
|
|
|
[19] |
YANG J Y, WANG G Q, ZHANG S. Impact of household quarantine on SARS-Cov-2 infection in mainland China: A mean-field modelling approach[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4500-4512. doi:10.3934/mbe.2020248
doi: 10.3934/mbe.2020248
|
|
|
[20] |
MUBAYI A, ZALETA C K, MARTCHEVA M. A cost-based comparison of quarantine strategies for new emerging diseases[J]. Mathematical Biosciences and Engineering, 2017, 7(3): 687-717.
|
|
|
[21] |
SATO H, NAKADA H, YAMAGUCHI R, et al. When should we intervene to control the 2009 influenza A(H1N1) pandemic[J]. Eurosurveillance: Europe′s Journal on Infectious Disease Surveillance,Epidemiology,Prevention and Control, 2010, 15(1):9-12. doi:10.2807/ese.15.01.19455-en
doi: 10.2807/ese.15.01.19455-en
|
|
|
[22] |
王霞,唐三一,陈勇,等. 新型冠状病毒肺炎疫情下武汉及周边地区何时复工?数据驱动的网络模型分析[J]. 中国科学: 数学,2020,50(7): 969-978. doi:10.1360/ssm-2020-0037 WANG X, TANG S Y, CHEN Y, et al. When will be the resumption of work in Wuhan and its surrounding areas during COVID-19 epidemic? A data-driven network modeling analysis[J]. Scientia Sinica: Mathematica, 2020, 50(7): 969-978. doi:10.1360/ssm-2020-0037
doi: 10.1360/ssm-2020-0037
|
|
|
[23] |
YUAN R G, MA Y J, SHEN C C, et al. Global dynamics of COVID-19 epidemic model with recessive infection and isolation[J]. Mathematical Biosciences and Engineering, 2021, 18(2): 1833-1844. doi:10.3934/mbe.2021095
doi: 10.3934/mbe.2021095
|
|
|
[24] |
黄森忠,彭志行,靳祯. 新型冠状病毒肺炎疫情控制策略研究:效率评估及建议[J]. 中国科学:数学,2020,50(6): 885-898. doi:10.1360/ssm-2020-0043 HUANG S H, PENG Z H, JIN Z. Studies of the strategies for controlling the COVID-19 epidemic in China: Estimation of control efficacy and suggestions for policy makers[J]. Scientia Sinica: Mathematica, 2020, 50(6): 885-898. doi:10.1360/ssm-2020-0043
doi: 10.1360/ssm-2020-0043
|
|
|
[25] |
WANG K, LU Z Z, WANG X M, et al. Current trends and future prediction of novel coronavirus disease (COVID-19) epidemic in China: A dynamical modeling analysis[J].Mathematical Biosciences and Engineering, 2020, 17(4): 3052-3061. doi:10.3934/mbe.2020173
doi: 10.3934/mbe.2020173
|
|
|
[26] |
张仲华. 具一般非线性隔离函数和接触率的染病年龄SIRS模型平衡点的存在性及稳定性[J]. 高校应用数学学报, 2011, 26(1): 46-54. ZHANG Z H. Existence and stability of equilibria for an infection-age dependent SIRS epidemic model with general nonlinear contact rate and screening function[J]. Applied Mathematics A Journal of Chinese Universities, 2011, 26(1): 46-54.
|
|
|
[27] |
ZHANG T L, TENG Z D. On a nonautonomous SEIRS model in epidemiology[J].Bulletin of Mathematical Biology, 2007, 69(8): 2537-2559. doi:10.1007/s11538-007-9231-z
doi: 10.1007/s11538-007-9231-z
|
|
|
[28] |
ZHAO X Q. Basic reproduction ratios for periodic compartmental models with time delay[J]. Journal of Dynamics and Differential Equations, 2017, 29: 67-82. doi:10.1007/s10884-015-9425-2
doi: 10.1007/s10884-015-9425-2
|
|
|
[29] |
NIU X G, ZHANG T L, TENG Z D. The asymptotic behavior of a nonautonomous eco-epidemic model with disease in the prey[J]. Applied Mathematical Modelling, 2011, 35(1): 457-470. doi:10.1016/j.apm.2010.07.010
doi: 10.1016/j.apm.2010.07.010
|
|
|
[30] |
SMITH H L, ZHAO X Q. Robust persistence for semidynamical systems[J]. Nonlinear Analysis Theory Methods and Applications, 2001, 47(9):6169-6179. doi:10.1016/s0362-546x(01)00678-2
doi: 10.1016/s0362-546x(01)00678-2
|
|
|
[31] |
白娟,贾建文. 具有媒体报道影响的SIRS模型分析[J]. 应用数学,2018,31(1): 135-140. BAI J, JIA J W. Analysis of an SIRS model with the impact of media[J]. Mathematica Applicata, 2018, 31(1): 135-140.
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