Dynamics of cascades on burstiness-controlled temporal networks

TL;DR

This paper develops a master equation framework to analyze how burstiness in temporal networks influences the speed and nature of information and epidemic spreading, revealing universal behaviors and nuanced effects.

Contribution

It introduces a novel analytical approach to model burstiness effects on cascades in temporal networks using renewal processes, bridging a gap in understanding complex dynamics.

Findings

Increasing interevent time variance can both accelerate and decelerate threshold-based spreading.

Interevent time skewness leads to universal spreading time curves.

Burstiness generally decelerates epidemic spreading.

Abstract

Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic dynamics is lacking. We develop a master equation formalism to study cascades on temporal networks with burstiness modelled by renewal processes. Supported by numerical and data-driven simulations, we describe the interplay between heterogeneous temporal interactions and models of threshold-driven and epidemic spreading. We find that increasing interevent time variance can both accelerate and decelerate spreading for threshold models, but can only decelerate epidemic spreading. When accounting for the skewness of different interevent time distributions, spreading times collapse onto a universal curve. Our framework uncovers a deep yet subtle connection between generic diffusion mechanisms and underlying temporal network structures that impacts on a broad class of networked phenomena, from spin interactions to epidemic contagion and language dynamics.