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

TL;DR

This paper investigates the numerical challenges in studying epidemic and percolation transitions on networks, highlighting key subtleties for accurately estimating critical points and properties in simulations.

Contribution

It identifies and analyzes the subtleties involved in numerical simulations of epidemic models on networks, clarifying how to correctly detect criticality.

Findings

Identification of criticality detectors for epidemic models

Analysis of subtleties affecting transition point estimation

Guidelines for accurate numerical simulation of network percolation

Abstract

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.