High-accuracy approximation of binary-state dynamics on networks

TL;DR

This paper introduces a master equation approach for accurately approximating binary-state dynamics on networks, improving upon traditional mean-field methods for applications like epidemic thresholds and spin models.

Contribution

It presents a master equation framework that generalizes and improves the accuracy of existing mean-field and pairwise theories for binary-state network dynamics.

Findings

Master equations provide highly accurate approximations.

Standard mean-field theories are derived as approximate solutions.

Applications include precise epidemic thresholds and critical points.

Abstract

Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories are shown to result from seeking approximate solutions of the master equations. Applications to the calculation of SIS epidemic thresholds and critical points of non-equilibrium spin models are also demonstrated.