Influential spreaders for recurrent epidemics on networks

The identification of which nodes are optimal seeds for spreading processes on a network is a nontrivial problem that has attracted much interest recently. While activity has mostly focused on the nonrecurrent 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 D. B. Larremore [Phys. Rev. E 85, 066131 (2012)PLEEE81539-375510.1103/PhysRevE.85.066131] 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. A comparison of these results with numerical simulations performed on synthetic networks with power-law degree distribution reveals, in general, good agreement in the subcritical regime, leaving thus some questions open for further investigation relative to the supercritical region.