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复杂网络上非马尔科夫易感-感染模型的二阶平均场求解

祁婷 林诏华 冯秘 唐明

祁婷, 林诏华, 冯秘, 唐明. 复杂网络上非马尔科夫易感-感染模型的二阶平均场求解[J]. 华东师范大学学报(自然科学版), 2021, (1): 144-151. doi: 10.3969/j.issn.1000-5641.20202s2001
引用本文: 祁婷, 林诏华, 冯秘, 唐明. 复杂网络上非马尔科夫易感-感染模型的二阶平均场求解[J]. 华东师范大学学报(自然科学版), 2021, (1): 144-151. doi: 10.3969/j.issn.1000-5641.20202s2001
QI Ting, LIN Zhaohua, FENG Mi, TANG Ming. Second order mean field approach of non-Markovian susceptible-infected model for complex networks[J]. Journal of East China Normal University (Natural Sciences), 2021, (1): 144-151. doi: 10.3969/j.issn.1000-5641.20202s2001
Citation: QI Ting, LIN Zhaohua, FENG Mi, TANG Ming. Second order mean field approach of non-Markovian susceptible-infected model for complex networks[J]. Journal of East China Normal University (Natural Sciences), 2021, (1): 144-151. doi: 10.3969/j.issn.1000-5641.20202s2001

复杂网络上非马尔科夫易感-感染模型的二阶平均场求解

doi: 10.3969/j.issn.1000-5641.20202s2001
基金项目: 国家自然科学基金(11975099, 11575041)
详细信息
    通讯作者:

    唐 明, 男, 研究员, 博士生导师, 研究方向为复杂网络科学. E-mail: mtang@ce.ecnu.edu.cn

  • 中图分类号: O415.6

Second order mean field approach of non-Markovian susceptible-infected model for complex networks

  • 摘要: 提出了一种能够描述网络传播过程的非马尔科夫特征的数学理论, 从而为控制真实世界中疾病或谣言的扩散提供理论支撑. 根据二阶平均场近似的方法, 以及通过引入闲置边的概念, 给出了能够在复杂网络上求解易感-感染(Susceptible-Infected, SI)非马尔科夫传播动力学的一系列偏微分方程组. 比较了实验模拟结果与理论计算结果, 该数学方法能够精准预测复杂网络上 SI 模型的爆发时间演化过程. 另外, 该理论还可以用来预测单个节点被感染的平均时刻, 且通过实验模拟结果证实了其正确性和准确性.
  • 图  1  闲置边示意图

    Fig.  1  Schematic diagram of idle edges

    图  2  韦布尔分布

    Fig.  2  Weibull distribution

    图  3  SI模型理论与模拟对比图

    Fig.  3  Comparison between the theory and simulation of the SI model

    图  4  真实网络中不同参数下各个节点被感染平均时刻

    Fig.  4  Average time for a single node to be infected in real networks with different parameters

  • [1] PASTOR-SATORRAS R, VESPIGNANI A. Epidemic Spreading in Scale-Free Networks [J]. Physical Review Letters, 2001, 86(14): 3200-3203.
    [2] PASTOR-SATORRAS R, CASTELLANO C, VAN MIEGHEM P, et al. Epidemic processes in complex networks [J]. Reviews of Modern Physics, 2015, 87(3): 925.
    [3] WANG W, TANG M, STANLEY H E, et al. Unification of theoretical approaches for epidemic spreading on complex networks [J]. Reports on Progress in Physics, 2017, 80(3): 036603.
    [4] BARABÁSI, A L. The origin of bursts and heavy tails in human dynamics [J]. Nature, 2005, 435(7039): 207.
    [5] STOUFFER D B, MALMGREN R D, AMARAL L A N. Comment on Barabasi [J]. Nature, 2005, 435: 207-211.
    [6] VÁZQUEZ A, OLIVEIRA J G, DEZSÖ Z, et al. Modeling bursts and heavy tails in human dynamics [J]. Physical Review E, 2006, 73(3): 036127.
    [7] KENAH E, ROBINS J M. Second look at the spread of epidemics on networks [J]. Physical Review E, 2007, 76(3): 036113.
    [8] VAZQUEZ A, RACZ B, LUKACS A, et al. Impact of non-Poissonian activity patterns on spreading processes [J]. Physical Review Letters, 2007, 98(15): 158702.
    [9] KARRER B, NEWMAN M E J. Message passing approach for general epidemic models [J]. Physical Review E, 2010, 82(1): 016101.
    [10] MIN B, GOH K I, VAZQUEZ A. Spreading dynamics following bursty human activity patterns [J]. Physical Review E, 2015, 83(3): 036102.
    [11] STARNINI M, GLEESON J P, BOGUÑÁ M. Equivalence between non-Markovian and Markovian dynamics in epidemic spreading processes [J]. Physical Review Letters, 2017, 118(12): 128301.
    [12] CATOR E, BOVENKAMP R V D, VAN MIEGHEM P. Susceptible-infected-susceptible epidemics on networks with general infection and cure times [J]. Physical Review E, 2013, 87(6): 1-7.
    [13] FENG M, CAI S M, TANG M, et al. Equivalence and its invalidation between non-Markovian and Markovian spreading dynamics on complex networks [J]. Nature Communications, 2019, 10(1): 1-10.
    [14] MIN B, GOH K I, KIM I M. Suppression of epidemic outbreaks with heavy-tailed contact dynamics [J]. Europhysics Letters, 2013, 103(5): 50002.
    [15] VANMIEGHEM P, VANDEBOVENKAMP R. Non-Markovian infection spread dramatically alters the susceptible-infected-susceptible epidemic threshold in networks [J]. Physical Review Letters, 2013, 110(10): 108701.
    [16] GEORGIOU N, KISS I Z, SCALAS E. Solvable non-Markovian dynamic network [J]. Physical Review E, 2015, 92(4): 042801.
    [17] KISS I Z, RÖST G, VIZI Z. Generalization of pairwise models to non-Markovian epidemics on networks [J]. Physical Review Letters, 2015, 115(7): 078701.
    [18] SHERBORNE N, MILLER J C, BLYUSS K B, et al. Mean-field models for non-Markovian epidemics on networks [J]. Journal of Mathematical Biology, 2018, 76(3): 755-778.
    [19] ANDERSON R M, MAY R M. Infectious Diseases of Humans: Dynamics and Control[M]. Oxford University Press, 1992.
    [20] VANMIEGHEM P, OMIC J, KOOIJ R. Virus spread in networks [J]. IEEE/ACM Transactions On Networking, 2009, 17(1): 1-14.
    [21] VANMIEGHEM P. The n-intertwined SIS epidemic network model [J]. Computing, 2011, 93(2-4): 147-169.
    [22] MCGLADE J M. Advanced Ecological Theory: Principles and Applications[M]. Hoboken: John Wiley & Sons, Ltd, 1999.
    [23] KEELING M J. The effects of local spatial structure on epidemiological invasions [J]. Proceedings of the Royal Society B: Biological Sciences, 1999, 266(1421): 859-867.
    [24] ROBINSON J C, GLENDINNING P A. From Finite to Infinite Dimensional Dynamical Systems[M]. Berlin: Springer Science & Business Media, 2001.
    [25] EAMES K T D, KEELING M J. Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases [J]. Proceedings of the National Academy of Sciences, 2002, 99(20): 13330-13335.
    [26] GLEESON J P. High-accuracy approximation of Binary-State dynamics on networks [J]. Physical Review Letters, 2011, 107(6): 068701.
    [27] ZACHARY W. An information flow model for conflict and fission in small groups [J]. Journal of Anthropological Research, 1977, 33(4): 452-473.
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出版历程
  • 收稿日期:  2020-03-03
  • 刊出日期:  2021-01-27

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