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

Mi Feng, Shi Min Cai, Ming Tang, Ying Cheng Lai

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish (US)
Article number3748
JournalNature communications
Issue number1
StatePublished - Dec 1 2019

ASJC Scopus subject areas

  • Chemistry(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Physics and Astronomy(all)


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