Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks

TL;DR

This paper develops a pair quenched mean-field theory for the SIS epidemic model on complex networks, accurately predicting epidemic thresholds by incorporating dynamical correlations, and demonstrates its effectiveness through analytical and numerical results.

Contribution

It introduces a pair quenched mean-field approach that improves threshold predictions for SIS dynamics on large networks by accounting for correlations.

Findings

The theory provides analytical thresholds for star and wheel graphs.

Numerical thresholds for power-law networks are obtained via eigenvalue problems.

The pair QMF theory outperforms simpler models in accuracy.

Abstract

We present a quenched mean-field (QMF) theory for the dynamics of the susceptible-infected-susceptible (SIS) epidemic model on complex networks where dynamical correlations between connected vertices are taken into account by means of a pair approximation. We present analytical expressions of the epidemic thresholds in the star and wheel graphs and in random regular networks. For random networks with a power law degree distribution, the thresholds are numerically determined via an eigenvalue problem. The pair and one-vertex QMF theories yield the same scaling for the thresholds as functions of the network size. However, comparisons with quasi-stationary simulations of the SIS dynamics on large networks show that the former is quantitatively much more accurate than the latter. Our results demonstrate the central role played by dynamical correlations on the epidemic spreading and introduce an efficient way to theoretically access the thresholds of very large networks that can be extended to dynamical processes in general.