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Equivalence and its invalidation between non-Markovian and Markovian spreading dynamics on complex networks

Author

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  • Mi Feng

    (East China Normal University
    University of Electronic Science and Technology of China
    University of Electronic Science and Technology of China)

  • Shi-Min Cai

    (University of Electronic Science and Technology of China
    University of Electronic Science and Technology of China)

  • Ming Tang

    (East China Normal University
    East China Normal University)

  • Ying-Cheng Lai

    (Arizona State University)

Abstract

Epidemic spreading processes in the real world depend on human behaviors and, consequently, are typically non-Markovian in that the key events underlying the spreading dynamics cannot be described as a Poisson random process and the corresponding event time is not exponentially distributed. In contrast to Markovian type of spreading dynamics for which mathematical theories have been well developed, we lack a comprehensive framework to analyze and fully understand non-Markovian spreading processes. Here we develop a mean-field theory to address this challenge, and demonstrate that the theory enables accurate prediction of both the transient phase and the steady states of non-Markovian susceptible-infected-susceptible spreading dynamics on synthetic and empirical networks. We further find that the existence of equivalence between non-Markovian and Markovian spreading depends on a specific edge activation mechanism. In particular, when temporal correlations are absent on active edges, the equivalence can be expected; otherwise, an exact equivalence no longer holds.

Suggested Citation

  • Mi Feng & Shi-Min Cai & Ming Tang & Ying-Cheng Lai, 2019. "Equivalence and its invalidation between non-Markovian and Markovian spreading dynamics on complex networks," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    • Handle: RePEc:nat:natcom:v:10:y:2019:i:1:d:10.1038_s41467-019-11763-z
    DOI: 10.1038/s41467-019-11763-z
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    Cited by:

    1. Zhu, Yanpeng & Chen, Lei & Jia, Chun-Xiao & Meng, Fanyuan & Liu, Run-Ran, 2023. "Non-Markovian node fragility in cascading failures on random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    2. Wu, Dayu & Liu, Ying & Tang, Ming & Xu, Xiao-Ke & Guan, Shuguang, 2022. "Impact of hopping characteristics of inter-layer commuters on epidemic spreading in multilayer networks," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Tomovski, Igor & Basnarkov, Lasko & Abazi, Alajdin, 2022. "Endemic state equivalence between non-Markovian SEIS and Markovian SIS model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    4. Basnarkov, Lasko & Tomovski, Igor & Sandev, Trifce & Kocarev, Ljupco, 2022. "Non-Markovian SIR epidemic spreading model of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    5. Wang, Haiying & Moore, Jack Murdoch & Small, Michael & Wang, Jun & Yang, Huijie & Gu, Changgui, 2022. "Epidemic dynamics on higher-dimensional small world networks," Applied Mathematics and Computation, Elsevier, vol. 421(C).

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