Modelling and Bayesian analysis of the Abakaliki Smallpox Data

TL;DR

This paper presents the first full Bayesian analysis of the complete Abakaliki smallpox data using data-augmentation MCMC methods, providing detailed estimates of infection dynamics without likelihood approximations.

Contribution

It introduces a novel Bayesian approach with data-augmentation MCMC for analyzing the full smallpox dataset, avoiding previous approximation methods.

Findings

Estimates of basic model parameters and reproduction numbers.

Reconstructed likely infection paths.

Model validation through simulation-based assessment.

Abstract

The celebrated Abakaliki smallpox data have appeared numerous times in the epidemic modelling literature, but in almost all cases only a specific subset of the data is considered. There is one previous analysis of the full data set, but this relies on approximation methods to derive a likelihood. The data themselves continue to be of interest due to concerns about the possible re-emergence of smallpox as a bioterrorism weapon. We present the first full Bayesian analysis using data-augmentation Markov chain Monte Carlo methods which avoid the need for likelihood approximations. Results include estimates of basic model parameters as well as reproduction numbers and the likely path of infection. Model assessment is carried out using simulation-based methods.