The Effect of Concurrency on Epidemic Threshold in Time-Varying Networks

  • Tomokatsu Onaga
  • James P. Gleeson
  • Naoki MasudaEmail author
Part of the Computational Social Sciences book series (CSS)


Various epidemic spreading processes are considered to take place on time-varying networks. One key factor that alters epidemic spreading on time-varying networks is concurrency, the number of neighbours that a node has at a given time point. In this chapter, we present a theoretical study of the effects of concurrency on the susceptible-infected-susceptible epidemic processes on a class of temporal network models. By theoretical analysis that explicitly takes into account stochastic dying-out effects, we show that network dynamics increase the epidemic threshold (i.e., suppress epidemics), compared to that for the time-averaged network when the nodes’ concurrency is low, but also decrease the epidemic threshold (i.e., enhance epidemics) when the concurrency is high.


SIS model Concurrency Epidemic threshold Phase transition Activity-driven model Stochastic extinction 



T.O. acknowledges the support provided through JSPS KAKENHI Grant Number JP19K14618 and JP19H01506. J.G. acknowledges the support provided through Science Foundation Ireland (Grants No. 16/IA/4470 and No. 16/RC/3918). N.M. acknowledges the support provided through JST, CREST, and JST, ERATO, Kawarabayashi Large Graph Project.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tomokatsu Onaga
    • 1
  • James P. Gleeson
    • 2
  • Naoki Masuda
    • 3
    Email author
  1. 1.The Frontier Research Institute for Interdisciplinary Sciences and Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.MACSI, Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland
  3. 3.Department of Engineering MathematicsUniversity of BristolBristolUK

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