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Spreading dynamics following bursty human activity patterns

Byungjoon Min1, K.-I. Goh1, and Alexei Vazquez2

  • 1Department of Physics, Korea University, Seoul 136-713, Korea
  • 2Department of Radiation Oncology, The Cancer Institute of New Jersey and UMDNJ–Robert Wood Johnson Medical School, New Brunswick, New Jersey 08540, USA

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Phys. Rev. E 83, 036102 – Published 7 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.036102

Abstract

We study the susceptible-infected model with power-law waiting time distributions P(τ)~τ−α, as a model of spreading dynamics under heterogeneous human activity patterns. We found that the average number of new infections n(t) at time t decays as a power law in the long-time limit, n(t)~t−β, leading to extremely slow prevalence decay. We also found that the exponent in the spreading dynamics β is related to that in the waiting time distribution α in a way depending on the interactions between agents but insensitive to the network topology. These observations are well supported by both the theoretical predictions and the long prevalence decay time in real social spreading phenomena. Our results unify individual activity patterns with macroscopic collective dynamics at the network level.

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Outline

Information

Phys. Rev. E 83, 036102– Published 7 March, 2011
  • Received 16 June 2010

©2011 American Physical Society

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