A Gaussian-process approximation to a spatial SIR process using moment closures and emulators

TL;DR

This paper introduces a Gaussian process-based approximation for spatial SIR disease models, combining moment-closure and emulators to efficiently infer disease spread across locations from noisy data.

Contribution

It develops a novel Gaussian process approximation for a spatial SIR process using moment closures and emulators, enabling scalable inference from spatial infection data.

Findings

Successfully modeled simulated spatial infections.

Applied to real Zika infection data in Brazil.

Demonstrated efficient inference with noisy, underreported counts.

Abstract

The dynamics that govern disease spread are hard to model because infections are functions of both the underlying pathogen as well as human or animal behavior. This challenge is increased when modeling how diseases spread between different spatial locations. Many proposed spatial epidemiological models require trade-offs to fit, either by abstracting away theoretical spread dynamics, fitting a deterministic model, or by requiring large computational resources for many simulations. We propose an approach that approximates the complex spatial spread dynamics with a Gaussian process. We first propose a flexible spatial extension to the well-known SIR stochastic process, and then we derive a moment-closure approximation to this stochastic process. This moment-closure approximation yields ordinary differential equations for the evolution of the means and covariances of the susceptibles and infectious through time. Because these ODEs are a bottleneck to fitting our model by MCMC, we approximate them using a low-rank emulator. This approximation serves as the basis for our hierarchical model for noisy, underreported counts of new infections by spatial location and time. We demonstrate using our model to conduct inference on simulated infections from the underlying, true spatial SIR jump process. We then apply our method to model counts of new Zika infections in Brazil from late 2015 through early 2016.