Bayesian inference of epidemics on networks via belief propagation

Phys Rev Lett. 2014 Mar 21;112(11):118701. doi: 10.1103/PhysRevLett.112.118701. Epub 2014 Mar 17.


We study several Bayesian inference problems for irreversible stochastic epidemic models on networks from a statistical physics viewpoint. We derive equations which allow us 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 susceptible-infected-recovered or susceptible-infected 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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Bayes Theorem*
  • Contact Tracing / methods*
  • Epidemiologic Methods*
  • Models, Statistical*
  • Stochastic Processes