Susceptible-infected-susceptible dynamics on the rewired configuration model

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 $k_{\max }\to \infty$, a generalization of the result obtained with quenched mean-field theory for static networks.

Main text: 4 pages, 3 figures. Supplemental material: 6 pages