Collective versus hub activation of epidemic phases on networks

TL;DR

This paper introduces a criterion to distinguish whether epidemic thresholds on scale-free networks are driven by hubs or collective effects, validated across models and network types, revealing new insights into epidemic phase transitions.

Contribution

It proposes a general criterion to identify the nature of epidemic thresholds on scale-free networks, contrasting hub-driven and collective activation mechanisms.

Findings

Hubbing activation leads to zero threshold in the thermodynamic limit.

Waning immunity results in finite thresholds in certain scale-free networks.

The criterion is validated on synthetic and real networks across various models.

Abstract

We consider a general criterion to discern the nature of the threshold in epidemic models on scale-free (SF) networks. Comparing the epidemic lifespan of the nodes with largest degrees with the infection time between them, we propose a general dual scenario, in which the epidemic transition is either ruled by a hub activation process, leading to a null threshold in the thermodynamic limit, or given by a collective activation process, corresponding to a standard phase transition with a finite threshold. We validate the proposed criterion applying it to different epidemic models, with waning immunity or heterogeneous infection rates in both synthetic and real SF networks. In particular, a waning immunity, irrespective of its strength, leads to collective activation with finite threshold in scale-free networks with large exponent, at odds with canonical theoretical approaches.