  Recent work has shown that different theoretical approaches to the dynamics
of the Susceptible-Infected-Susceptible (SIS) model for epidemics lead to
qualitatively different estimates for the position of the epidemic threshold in
networks. Here we present large-scale numerical simulations of the SIS dynamics
on various types of networks, allowing the precise determination of the
effective threshold for systems of finite size N. We compare quantitatively the
numerical thresholds with theoretical predictions of the heterogeneous
mean-field theory and of the quenched mean-field theory. We show that the
latter is in general more accurate, scaling with N with the correct exponent,
but often failing to capture the correct prefactor.

Statistical Mechanics;Social and Information Networks;Physics and Society