Inference of epidemiological parameters from household stratified data

TL;DR

This paper develops Bayesian inference methods to estimate epidemiological parameters in a household-structured SIR model using early epidemic data, comparing exact and approximate approaches for efficiency and accuracy.

Contribution

It introduces two Bayesian MCMC methods for inferring transmission and recovery parameters from household-level infection data, with one being an efficient approximation.

Findings

Branching process approximation is highly accurate.

Approximate Bayesian inference is computationally efficient.

Methods effectively estimate key epidemic parameters.

Abstract

We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household transmission, recovery, and between-household transmission---from data of the day upon which each individual became infectious and the household in which each infection occurred, as would be available from first few hundred studies. Each method is a form of Bayesian Markov Chain Monte Carlo that allows us to calculate a joint posterior distribution for all parameters and hence the household reproduction number and the early growth rate of the epidemic. The first method performs exact Bayesian inference using a standard data-augmentation approach; the second performs approximate Bayesian inference based on a likelihood approximation derived from branching processes. These methods are compared for computational efficiency and posteriors from each are compared. The branching process is shown to be an excellent approximation and remains computationally efficient as the amount of data is increased.