High prevalence regimes in the pair quenched mean-field theory for the susceptible-infected-susceptible model on networks

TL;DR

This paper evaluates the pair quenched mean-field (PQMF) theory's accuracy in predicting SIS epidemic dynamics on networks, showing it outperforms standard QMF especially away from epidemic thresholds, with implications for high prevalence regimes.

Contribution

The study provides a comprehensive nonperturbative numerical analysis demonstrating the effectiveness of PQMF over QMF in diverse network structures for SIS models.

Findings

PQMF significantly outperforms QMF on synthetic networks.

PQMF provides highly accurate predictions away from epidemic thresholds.

Correlations between accuracy and average shortest path are observed.

Abstract

Reckoning of pairwise dynamical correlations significantly improves the accuracy of mean-field theories and plays an important role in the investigation of dynamical processes on complex networks. In this work, we perform a nonperturbative numerical analysis of the quenched mean-field theory (QMF) and the inclusion of dynamical correlations by means of the pair quenched mean-field (PQMF) theory for the susceptible-infected-susceptible (SIS) model on synthetic and real networks. We show that the PQMF considerably outperforms the standard QMF on synthetic networks of distinct levels of heterogeneity and degree correlations, providing extremely accurate predictions when the system is not too close to the epidemic threshold while the QMF theory deviates substantially from simulations for networks with a degree exponent $\gamma>2.5$. The scenario for real networks is more complicated, still with PQMF significantly outperforming the QMF theory. However, despite of high accuracy for most investigated networks, in a few cases PQMF deviations from simulations are not negligible. We found correlations between accuracy and average shortest path while other basic networks metrics seem to be uncorrelated with the theory accuracy. Our results show the viability of the PQMF theory to investigate the high prevalence regimes of recurrent-state epidemic processes on networks, a regime of high applicability.