Transmission parameters estimated for Salmonella typhimurium in swine using susceptible-infectious-resistant models and a Bayesian approach

Desirable BUGS in models of infectious diseases

Bayesian inference using Gibbs sampling (BUGS) is a set of statistical software that uses Markov chain Monte Carlo (MCMC) methods to estimate almost any specified model. Originally developed in the late 1980s, the software is an excellent introduction to applied Bayesian statistics without the need to write a MCMC sampler. The software is typically used for regression-based analyses, but any model that can be specified using graphical nodes are possible. Advanced topics such as missing data, spatial analysis, model comparison and dynamic infectious disease models can be tackled. Three examples are provided; a linear regression model to illustrate parameter estimation, the steps to ensure that the estimates have converged and a comparison of run-times across different computing platforms. The second example describes a model that estimates the probability of being vaccinated from cross-sectional and surveillance data, and illustrates the specification of different models, model comparison and data augmentation. The third example illustrates estimation of parameters within a dynamic Susceptible-Infected-Recovered model. These examples show that BUGS can be used to estimate parameters from models relevant for infectious diseases, and provide an overview of the relative merits of the approach taken.

A modified chain binomial model to analyse the ongoing measles epidemic in Greece, July 2017 to February 2018

Greece is currently experiencing a large measles outbreak, in the context of multiple similar outbreaks across Europe. We devised and applied a modified chain-binomial epidemic model, requiring very simple data, to estimate the transmission parameters of this outbreak. Model results indicate sustained measles transmission among the Greek Roma population, necessitating a targeted mass vaccination campaign to halt further spread of the epidemic. Our model may be useful for other countries facing similar measles outbreaks.

Birth/birth-death processes and their computable transition probabilities with biological applications

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth/birth-death process, a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution.