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

Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results