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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

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

doi: 10.3969/j.issn.1000-5641.20202s2001
  • Received Date: 2020-03-03
  • Publish Date: 2021-01-27
  • The objective of this paper is to propose a mathematical theory that can describe the non-Markovian characteristics of the network spreading process, thereby establishing theoretical support for controlling the propagation of diseases or rumors in the real world. According to the second-order mean-field approximation method and the concept of idle edges, a series of partial differential equations are presented that can be used to solve the non-Markovian spreading dynamics of a susceptible-infected (SI) model in complex networks. By comparing the simulation outputs with the theoretical results, this mathematical method can accurately predict the spreading process of the SI model on complex networks. The theory, moreover, can be used to predict the average time for a single node to be infected. The correctness and accuracy of the theory is verified by experimental simulation results.
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  • [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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