# Bayesian inference of epidemics on networks via Belief Propagation

arXiv: https://arxiv.org/abs/1307.6786 · HTML: https://mlsanity.com/paper/1307.6786/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2013.

## Built on by (most cited first, 4 of 4)

- [A Bayesian generative neural network framework for epidemic inference problems](https://mlsanity.com/paper/2111.03383/) (2021)
- [Effectiveness of probabilistic contact tracing in epidemic containment: the role of super-spreaders and transmission path reconstruction](https://mlsanity.com/paper/2312.00910/) (2023)
- [Evidence of Replica Symmetry Breaking under the Nishimori conditions in epidemic inference on graphs](https://mlsanity.com/paper/2502.13249/) (2025)
- [Gated Graph Neural Networks for Learning Hidden Independent Cascade Dynamics](https://mlsanity.com/paper/2610.04033/) (2026)

## Abstract (arXiv)

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.