Competing activation mechanisms in epidemics on networks

TL;DR

This paper investigates how different network structures and epidemic process types influence whether hubs or the network core primarily sustain epidemic activity, revealing a dual mechanism depending on network properties.

Contribution

It identifies the conditions under which either hubs or the network core dominate epidemic spreading, highlighting the impact of network correlations and degree distribution.

Findings

Innermost core boosts epidemics with transient states.

Hubs or core sustain steady-state epidemics depending on network properties.

Correlations in real networks can alter the dominant spreading mechanism.

Abstract

In contrast to previous common wisdom that epidemic activity in heterogeneous networks is dominated by the hubs with the largest number of connections, recent research has pointed out the role that the innermost, dense core of the network plays in sustaining epidemic processes. Here we show that the mechanism responsible of spreading depends on the nature of the process. Epidemics with a transient state are boosted by the innermost core. Contrarily, epidemics allowing a steady state present a dual scenario, where either the hub independently sustains activity and propagates it to the rest of the system, or, alternatively, the innermost network core collectively turns into the active state, maintaining it globally. In uncorrelated networks the former mechanism dominates if the degree distribution decays with an exponent larger than 5/2, and the latter otherwise. Topological correlations, rife in real networks, may perturb this picture, mixing the role of both mechanisms.