Susceptible-infected-susceptible dynamics on the rewired configuration model

TL;DR

This paper analyzes the susceptible-infected-susceptible epidemic dynamics on a rewired network model, deriving a unified threshold expression that interpolates between static and fully rewired regimes, revealing a vanishing epidemic threshold for large networks.

Contribution

It provides a unified analytical framework for SIS dynamics on networks with tunable edge rewiring, extending existing theories to intermediate regimes and large networks.

Findings

Derived a closed-form expression for the epidemic threshold at any rewiring rate.

Revealed that the threshold vanishes as the maximum degree grows infinitely large.

Unified previous results for static and annealed networks, improving their accuracy.

Abstract

We investigate the susceptible-infected-susceptible dynamics on configuration model networks. In an effort for the unification of current approaches, we consider a network whose edges are constantly being rearranged, with a tunable rewiring rate $\omega$. We perform a detailed stationary state analysis of the process, leading to a closed form expression of the absorbing-state threshold for an arbitrary rewiring rate. In both extreme regimes (annealed and quasi-static), we recover and further improve the results of current approaches, as well as providing a natural interpolation for the intermediate regimes. For any finite $\omega$, our analysis predicts a vanishing threshold when the maximal degree $k_\mathrm{max} \to \infty$, a generalization of the result obtained with quenched mean-field theory for static networks.