On the numerical study of percolation and epidemic critical properties in networks

The static properties of the fundamental model for epidemics of diseases allowing immunity (susceptible-infected-removed model) are known to be derivable by an exact mapping to bond percolation. Yet when performing numerical simulations of these dynamics in a network a number of subtleties must be taken into account in order to correctly estimate the transition point and the associated critical properties. We expose these subtleties and identify the different quantities which play the role of criticality detector in the two dynamics.