Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks

TL;DR

This paper analytically investigates the SIS epidemic model on networks, revealing how network topology and degree distribution influence the presence or absence of an epidemic threshold, especially in small-world networks.

Contribution

It provides a new analytical framework explaining the origin of epidemic threshold absence in heterogeneous networks, emphasizing the role of high-degree nodes and network topology.

Findings

Small-world networks with slow-decaying degree distributions lack an epidemic threshold.

The balance between high-degree nodes and their topological distance determines threshold presence.

The analytical approach clarifies the conditions under which epidemics can persist or die out.

Abstract

We develop an analytical approach to the susceptible-infected-susceptible (SIS) epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.