Bayesian inference of epidemics on networks via belief propagation.
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.
DISAT and Center for Computational Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy and Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri, Italy.
Fabrizio
F
Altarelli
DISAT and Center for Computational Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy and Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri, Italy and Human Genetics Foundation, Via Nizza 52, 10126 Torino, Italy.
Alfredo
A
Braunstein
DISAT and Center for Computational Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy and Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri, Italy.
Luca
L
Dall'Asta
Physics Faculty, Havana University, San Lazaro y L, 10400 Habana, Cuba.
Alejandro
A
Lage-Castellanos
DISAT and Center for Computational Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy and Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri, Italy and Human Genetics Foundation, Via Nizza 52, 10126 Torino, Italy.
Riccardo
R
Zecchina
D001499:Bayes Theorem; D016358:Contact Tracing / Q000379:methods*; D004812:Epidemiologic Methods; D015233:Models, Statistical; D013269:Stochastic Processes