Low prevalence, quasi-stationarity and power-law distribution in a model of spreading

TL;DR

This paper introduces a contagion spreading model that incorporates contagion quality and local dynamics, revealing low prevalence, quasi-stationarity, and power-law activity distributions consistent with empirical data.

Contribution

It presents a novel model accounting for contagion quality and local evaluation, capturing slow dynamics and activity distributions in complex networks.

Findings

Low prevalence across a range of contagion qualities.

Emergence of quasi-stationary states with exponential time scales.

Node activity follows a power-law distribution independent of network topology.

Abstract

Understanding how contagions (information, infections, etc) are spread on complex networks is important both from practical as well as theoretical point of view. Considerable work has been done in this regard in the past decade or so. However, most models are limited in their scope and as a result only capture general features of spreading phenomena. Here, we propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local (probabilistic) dynamics occurring at various nodes. Transmission occurs only after the quality-based fitness of the contagion has been evaluated by the local agent. The model exhibits quality-dependent exponential time scales at early times leading to a slowly evolving quasi-stationary state. Low prevalence is seen for a wide range of contagion quality for arbitrary large networks. We also investigate the activity of nodes and find a power-law distribution with a robust exponent independent of network topology. Our results are consistent with recent empirical observations.