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

Mi Feng, Shi-Min Cai, Ming Tang () and Ying-Cheng Lai
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Mi Feng: East China Normal University
Shi-Min Cai: University of Electronic Science and Technology of China
Ming Tang: East China Normal University
Ying-Cheng Lai: Arizona State University

Nature Communications, 2019, vol. 10, issue 1, 1-10

Abstract: 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.

Date: 2019
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DOI: 10.1038/s41467-019-11763-z

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