The zero-patient problem with noisy observations

Abstract

A Belief Propagation approach has been recently proposed for the zero-patient problem in a SIR epidemics. The zero-patient problem consists in finding the initial source of an epidemic outbreak given observations at a later time. In this work, we study a harder but related inference problem, in which observations are noisy and there is confusion between observed states. In addition to studying the zero-patient problem, we also tackle the problem of completing and correcting the observations possibly finding undiscovered infected individuals and false test results. Moreover, we devise a set of equations, based on the variational expression of the Bethe free energy, to find the zero patient along with maximum-likelihood epidemic parameters. We show, by means of simulated epidemics, how this method is able to infer details on the past history of an epidemic outbreak based solely on the topology of the contact network and a single snapshot of partial and noisy observations.

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• Detection of Rumors and Their Sources in Social Networks: A Comprehensive Survey
• The matrix product approximation for the dynamic cavity method
• Bayes-optimal inference for spreading processes on random networks
• Predicting epidemic evolution on contact networks from partial observations
• Morphological Inversion of Complex Diffusion
• Small-Coupling Dynamic Cavity: a Bayesian mean-field framework for epidemic inference
• A closure for the Master Equation starting from the Dynamic Cavity Method
• Minority Takeover in Majority Dynamics: Searching for Rare Initializations via the History Passing Algorithm
• Inference in Spreading Processes with Neural-Network Priors