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We consider the problem of model choice for stochastic epidemic models given partial observation of a disease outbreak through time. Our main focus is on the use of Bayes factors. Although Bayes factors have appeared in the epidemic modelling literature before, they can be hard to compute and little attention has been given to fundamental questions concerning their utility. In this paper we derive analytic expressions for Bayes factors given complete observation through time, which suggest practical guidelines for model choice problems. We extend the power posterior method for computing Bayes factors so as to account for missing data and apply this approach to partially observed epidemics. For comparison, we also explore the use of a deviance information criterion for missing data scenarios. The methods are illustrated via examples involving both simulated and real data.

The vast majority of models for the spread of communicable diseases are parametric in nature and involve underlying assumptions about how the disease spreads through a population. In this article we consider the use of Bayesian nonparametric approaches to analysing data from disease outbreaks. Specifically we focus on methods for estimating the infection process in simple models under the assumption that this process has an explicit time-dependence.

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.

Nosocomial pathogens such as Methicillin-Resistant {\em Staphylococcus aureus} (MRSA) and Vancomycin-resistant {\em Enterococci} (VRE) are the cause of significant morbidity and mortality among hospital patients. It is important to be able to assess the efficacy of control measures using data on patient outcomes. In this paper we describe methods for analysing such data using patient-level stochastic models which seek to describe the underlying unobserved process of transmission. The methods are applied to detailed longitudinal patient-level data on VRE from a study in a US hospital with eight intensive care units (ICUs). The data comprise admission and discharge dates, dates and results of screening tests, and dates during which precautionary measures were in place for each patient during the study period. Results include estimates of the efficacy of the control measures, the proportion of unobserved patients colonized with VRE and the proportion of patients colonized on admission.

This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious contacts, who are then removed if they have not been already after some tracing delay. The epidemic is analysed via an approximating, modified birth-death process, for which a type-reproduction number is derived in terms of unnamed individuals, that is shown to be infinite when the contact rate is sufficiently large. We obtain explicit results under the assumption of either constant or exponentially distributed infectious periods, including the epidemic extinction probability in the former case. Numerical illustrations show that, while the distributions of latent periods and delays have an effect on the spread of the epidemic, the assumption of whether the delays experienced by individuals infected by the same individual are of the same or independent length makes little difference., Comment: Mathematical Biosciences 2015

We describe a new method for evaluating Bayes factors. The key idea is to introduce a hypermodel in which the competing models are components of a mixture distribution. Inference for the mixing probabilities then yields estimates of the Bayes factors. Our motivation is the setting where the observed data are a partially observed realisation of a stochastic population process, although the methods have far wider applicability. The methods allow for missing data and for parameters to be shared between models. Illustrative examples including epidemics, population processes and regression models are given, showing that the methods are competitive compared to existing approaches.

Whole genome sequencing of pathogens from multiple hosts in an epidemic offers the potential to investigate who infected whom with unparalleled resolution, potentially yielding important insights into disease dynamics and the impact of control measures. We considered disease outbreaks in a setting with dense genomic sampling, and formulated stochastic epidemic models to investigate person-to-person transmission, based on observed genomic and epidemiological data. We constructed models in which the genetic distance between sampled genotypes depends on the epidemiological relationship between the hosts. A data augmented Markov chain Monte Carlo algorithm was used to sample over the transmission trees, providing a posterior probability for any given transmission route. We investigated the predictive performance of our methodology using simulated data, demonstrating high sensitivity and specificity, particularly for rapidly mutating pathogens with low transmissibility. We then analyzed data collected during an outbreak of methicillin-resistant Staphylococcus aureus in a hospital, identifying probable transmission routes and estimating epidemiological parameters. Our approach overcomes limitations of previous methods, providing a framework with the flexibility to allow for unobserved infection times, multiple independent introductions of the pathogen, and within-host genetic diversity, as well as allowing forward simulation.