Bayesian inference of epidemics on networks via Belief Propagation

TL;DR

This paper introduces a belief propagation-based Bayesian inference method for epidemic models on networks, capable of handling complex observation scenarios and outperforming previous approaches in accuracy.

Contribution

It develops a general, efficient, and exact on trees Bayesian inference framework for epidemic dynamics with diverse observation models, including unobserved nodes and mixed observation types.

Findings

Outperforms previous methods on synthetic networks

Accurately infers epidemic states with partial and varied observations

Efficiently computes posterior distributions for epidemic parameters

Abstract

We study several bayesian inference problems for irreversible stochastic epidemic models on networks from a statistical physics viewpoint. We derive equations which allow to accurately compute the posterior distribution of the time evolution of the state of each node given some observations. At difference with most existing methods, we allow very general observation models, including unobserved nodes, state observations made at different or unknown times, and observations of infection times, possibly mixed together. Our method, which is based on the Belief Propagation algorithm, is efficient, naturally distributed, and exact on trees. As a particular case, we consider the problem of finding the "zero patient" of a SIR or SI epidemic given a snapshot of the state of the network at a later unknown time. Numerical simulations show that our method outperforms previous ones on both synthetic and real networks, often by a very large margin.