Influential spreaders for recurrent epidemics on networks

TL;DR

This paper investigates the influence of individual nodes in recurrent epidemic spreading on networks, using avalanche theory to predict their impact on outbreak size and duration, especially near the epidemic threshold.

Contribution

It applies avalanche theory to the SIS model on networks, providing analytical predictions for node influence and highlighting the role of degree centrality.

Findings

Good agreement between theory and simulations in the subcritical regime

Analytical expressions derived for avalanche size and duration near the transition

Degree centrality significantly influences spreading influence

Abstract

The identification of which nodes are optimal seeds for spreading processes on a network is a non-trivial problem that has attracted much interest recently. While activity has mostly focused on non-recurrent type of dynamics, here we consider the problem for the Susceptible-Infected-Susceptible (SIS) spreading model, where an outbreak seeded in one node can originate an infinite activity avalanche. We apply the theoretical framework for avalanches on networks proposed by Larremore et al. [Phys. Rev. E 85, 066131 (2012)], to obtain detailed quantitative predictions for the spreading influence of individual nodes (in terms of avalanche duration and avalanche size) both above and below the epidemic threshold. When the approach is complemented with an annealed network approximation, we obtain fully analytical expressions for the observables of interest close to the transition, highlighting the role of degree centrality. Comparison of these results with numerical simulations performed on synthetic networks with power-law degree distribution reveals in general a good agreement in the subcritical regime, leaving thus some questions open for further investigation relative to the supercritical region.