Metapopulation models imply non-Poissonian statistics of interevent times

TL;DR

This paper demonstrates that heavy-tailed interevent time distributions in contact data naturally arise from basic metapopulation models, regardless of network structure or mobility rules, impacting contagion dynamics.

Contribution

It provides a theoretical link between simple metapopulation models and the heavy-tailed interevent times observed in real contact data, extending beyond specific network or mobility assumptions.

Findings

Heavy-tailed interevent times emerge from basic metapopulation models.

Results are valid for various mobility rules and network structures.

Implications for modeling contagion processes on networks.

Abstract

Interevent times in temporal contact data from humans and animals typically obey heavy-tailed distributions, and this property impacts contagion and other dynamical processes on networks. We theoretically show that distributions of interevent times heavier-tailed than exponential distributions are a consequence of the most basic metapopulation model used in epidemiology and ecology, in which individuals move from a patch to another according to the simple random walk. Our results hold true irrespectively of the network structure and also for more realistic mobility rules such as high-order random walks and the recurrent mobility patterns used for modeling human dynamics.