Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks.

We present a degree-based theoretical framework to study the susceptible-infected-susceptible (SIS) dynamics on time-varying (rewired) configuration model networks. Using this framework on a given degree distribution, we provide a detailed analysis of the stationary state using the rewiring rate to explore the whole range of the time variation of the structure relative to that of the SIS process. This analysis is suitable for the characterization of the phase transition and leads to three main contributions: (1) We obtain a self-consistent expression for the absorbing-state threshold, able to capture both collective and hub activation. (2) We recover the predictions of a number of existing approaches as limiting cases of our analysis, providing thereby a unifying point of view for the SIS dynamics on random networks. (3) We obtain bounds for the critical exponents of a number of quantities in the stationary state. This allows us to reinterpret the concept of hub-dominated phase transition. Within our framework, it appears as a heterogeneous critical phenomenon: observables for different degree classes have a different scaling with the infection rate. This phenomenon is followed by the successive activation of the degree classes beyond the epidemic threshold.