A Bayesian Nonparametric Analysis of the 2003 Outbreak of Highly Pathogenic Avian Influenza in the Netherlands

TL;DR

This paper introduces a Bayesian nonparametric approach to model and analyze the spread of avian influenza between farms, using spatial data and Gaussian Processes to inform disease control strategies.

Contribution

It develops a novel Bayesian nonparametric methodology with Gaussian Process priors for infection rates, enabling inference without parametric assumptions.

Findings

Inferred infection rates between farms based on spatial data.

Simulated effects of disease control strategies like ring-culling.

Found limited impact of ring-culling in high-density areas.

Abstract

Infectious diseases on farms pose both public and animal health risks, so understanding how they spread between farms is crucial for developing disease control strategies to prevent future outbreaks. We develop novel Bayesian nonparametric methodology to fit spatial stochastic transmission models in which the infection rate between any two farms is a function that depends on the distance between them, but without assuming a specified parametric form. Making nonparametric inference in this context is challenging since the likelihood function of the observed data is intractable because the underlying transmission process is unobserved. We adopt a fully Bayesian approach by assigning a transformed Gaussian Process prior distribution to the infection rate function, and then develop an efficient data augmentation Markov Chain Monte Carlo algorithm to perform Bayesian inference. We use the posterior predictive distribution to simulate the effect of different disease control methods and their economic impact. We analyse a large outbreak of Avian Influenza in the Netherlands and infer the between-farm infection rate, as well as the unknown infection status of farms which were pre-emptively culled. We use our results to analyse ring-culling strategies, and conclude that although effective, ring-culling has limited impact in high density areas.