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

TL;DR

This paper compares numerical simulations and theoretical predictions for the epidemic threshold in SIS models on networks, showing that quenched mean-field theory is generally more accurate than heterogeneous mean-field theory.

Contribution

It provides large-scale numerical results for SIS epidemic thresholds and evaluates the accuracy of different theoretical approaches on various network types.

Findings

Quenched mean-field theory generally predicts thresholds more accurately.

Numerical simulations reveal finite-size effects on epidemic thresholds.

Theoretical models differ in their ability to estimate the threshold's prefactor.

Abstract

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.