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arXiv · 2107.12665

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

Christoph Widder·Tanja Schilling
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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.

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Christoph Widder, Tanja Schilling. 2021-07-27. Generating functions for message-passing on weighted networks: directed bond percolation and SIR epidemics. https://doi.org/10.1103/physreve.104.054305

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