Generating functions for message-passing on weighted networks: directed bond percolation and SIR epidemics

TL;DR

This paper develops a message-passing framework to analyze SIR epidemic spreading on directed, weighted networks, predicting percolation thresholds, cluster sizes, and vaccination strategies with high accuracy on large, tree-like networks.

Contribution

It introduces a generating function approach for message-passing on weighted directed networks, providing rigorous bounds and accurate predictions for epidemic thresholds and cluster distributions.

Findings

Percolation threshold is a rigorous lower bound for real networks.

Predictions match well with numerical simulations on large, tree-like networks.

The method informs effective vaccination strategies.

Abstract

We study the SIR ("susceptible, infected, removed/recovered") model on directed graphs with heterogeneous transmission probabilities within the message-passing approximation. We characterize the percolation transition, predict cluster size distributions and suggest vaccination strategies. All predictions are compared to numerical simulations on real networks. The percolation threshold which we predict is a rigorous lower bound to the threshold on real networks. For large, locally tree-like networks, our predictions agree very well with the numerical data.