Modelling under-reporting in epidemics.

Under-reporting of infected cases is crucial for many diseases because of the bias it can introduce when making inference for the model parameters. The objective of this paper is to study the effect of under-reporting in epidemics by considering the stochastic Markovian SIR epidemic in which various reporting processes are incorporated. In particular, we first investigate the effect on the estimation process of ignoring under-reporting when it is present in an epidemic outbreak. We show that such an approach leads to under-estimation of the infection rate and the reproduction number. Secondly, by allowing for the fact that under-reporting is occurring, we develop suitable models for estimation of the epidemic parameters and explore how well the reporting rate and other model parameters can be estimated. We consider the case of a constant reporting probability and also more realistic assumptions which involve the reporting probability depending on time or the source of infection for each infected individual. Due to the incomplete nature of the data and reporting process, the Bayesian approach provides a natural modelling framework and we perform inference using data augmentation and reversible jump Markov chain Monte Carlo techniques.

Exact Bayesian inference of epidemiological parameters from mortality data: application to African swine fever virus.

Pathogens such as African swine fever virus (ASFV) are an increasing threat to global livestock production with implications for economic well-being and food security. Quantification of epidemiological parameters, such as transmission rates and latent and infectious periods, is critical to inform efficient disease control. Parameter estimation for livestock disease systems is often reliant upon transmission experiments, which provide valuable insights in the epidemiology of disease but which may also be unrepresentative of at-risk populations and incur economic and animal welfare costs. Routinely collected mortality data are a potential source of readily available and representative information regarding disease transmission early in outbreaks. We develop methodology to conduct exact Bayesian parameter inference from mortality data using reversible jump Markov chain Monte Carlo incorporating multiple routes of transmission (e.g. within-farm secondary and background transmission from external sources). We use this methodology to infer epidemiological parameters for ASFV using data from outbreaks on nine farms in the Russian Federation. This approach improves inference on transmission rates in comparison with previous methods based on approximate Bayesian computation, allows better estimation of time of introduction and could readily be applied to other outbreaks or pathogens.