Network Inference from Population-Level Observation of Epidemics

TL;DR

This paper presents a Bayesian method to infer the class of underlying networks from population-level epidemic data, using a surrogate birth-death process to approximate epidemic dynamics.

Contribution

It introduces a novel approach combining epidemic modeling and Bayesian inference to classify network types from limited population-level data.

Findings

Accurately classifies network types on synthetic data

Works effectively on real-world epidemic data

Uses a surrogate model for efficient inference

Abstract

Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem of inferring the class of the underlying network when epidemic data is only available at population-level (i.e. the number of infected individuals at a finite set of discrete times of a single realisation of the epidemic), the only information likely to be available in real world settings. To tackle this, epidemics on networks are approximated by a Birth-and-Death process which keeps track of the number of infected nodes at population level. The rates of this surrogate model encode both the structure of the underlying network and disease dynamics. We use extensive simulations over Regular, Erd\H{o}s-R\'enyi and Barab\'asi-Albert networks to build network class-specific priors for these rates. % show that different well-known network classes map onto distinct regions of the parameter space of this model. We then use Bayesian model selection to recover the most likely underlying network class, based only on a single realisation of the epidemic. We show that the proposed methodology yields good results on both synthetic and real-world networks.