Metastable Localization of Diseases in Complex Networks

TL;DR

This paper investigates how diseases localize around hubs in complex networks within the SIS epidemic model, revealing metastable localized states below the epidemic threshold and a smooth transition to delocalization.

Contribution

It introduces the concept of metastable localization in epidemic spreading on heterogeneous networks and analyzes how this phenomenon can be detected and characterized.

Findings

Localized states are metastable below the epidemic threshold.

The transition from localized to delocalized states is smooth, not sharp.

Localization can be detected from the distribution of infective nodes.

Abstract

We describe the phenomenon of localization in the epidemic SIS model on highly heterogeneous networks in which strongly connected nodes (hubs) play the role of centers of localization. We find that in this model the localized states below the epidemic threshold are metastable. The longevity and scale of the metastable outbreaks do not show a sharp localization transition, instead there is a smooth crossover from localized to delocalized states as we approach the epidemic threshold from below. Analyzing these long-lasting local outbreaks for a random regular graph with a hub, we show how this localization can be detected from the shape of the distribution of the number of infective nodes.