Contagion dynamics in time-varying metapopulation networks

TL;DR

This paper investigates how contagion spreads in time-varying metapopulation networks, revealing that dynamic connections significantly alter epidemic thresholds and spreading speed compared to static networks.

Contribution

It analytically derives the epidemic threshold for SIR processes on activity-driven time-varying networks, highlighting differences from static network models.

Findings

Mobility threshold depends on dynamic parameters, not static network properties.

Contagion spreads slower in time-varying networks than in static counterparts.

Time-varying networks require higher mobility for epidemic onset.

Abstract

The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups or patches are often represented as nodes in a network whose links represent the migration routes among them. The connections have been so far mostly considered as static, but in general evolve in time. Here we address this case by investigating simple contagion processes on time-varying metapopulation networks. We focus on the SIR process and determine analytically the mobility threshold for the onset of an epidemic spreading in the framework of activity-driven network models. We find profound differences from the case of static networks. The threshold is entirely described by the dynamical parameters defining the average number of instantaneously migrating individuals and does not depend on the properties of the static network representation. Remarkably, the diffusion and contagion processes are slower in time-varying graphs than in their aggregated static counterparts, the mobility threshold being even two orders of magnitude larger in the first case. The presented results confirm the importance of considering the time-varying nature of complex networks.