Quantitative Epidemiology: A Bayesian Perspective
AuthorZarebski, Alexander Eugene
AffiliationSchool of Mathematics and Statistics
Document TypePhD thesis
Access StatusOpen Access
© Alexander Eugene Zarebski
Influenza inflicts a substantial burden on society but accurate and timely forecasts of seasonal epidemics can help mitigate this burden by informing interventions to reduce transmission. Recently, both statistical (correlative) and mechanistic (causal) models have been used to forecast epidemics. However, since mechanistic models are based on the causal process underlying the epidemic they are poised to be more useful in the design of intervention strategies. This study investigate approaches to improve epidemic forecasting using mechanistic models. In particular, it reports on efforts to improve a forecasting system targeting seasonal influenza epidemics in major cities across Australia. To improve the forecasting system we first needed a way to benchmark its performance. We investigate model selection in the context of forecasting, deriving a novel method which extends the notion of Bayes factors to a predictive setting. Applying this methodology we found that accounting for seasonal variation in absolute humidity improves forecasts of seasonal influenza in Melbourne, Australia. This result holds even when accounting for the uncertainty in predicting seasonal variation in absolute humidity. Our initial attempts to forecast influenza transmission with mechanistic models were hampered by high levels of uncertainty in forecasts produced early in the season. While substantial uncertainty seems inextricable from long-term prediction, it seemed plausible that historical data could assist in reducing this uncertainty. We define a class of prior distributions which simplify the process of incorporating existing knowledge into an analysis, and in doing so offer a refined interpretation of the prior distribution. As an example we used historical time series of influenza epidemics to reduce initial uncertainty in forecasts for Sydney, Australia. We explore potential pitfalls that may be encountered when using this class of prior distribution. Deviating from the theme of forecasting, we consider the use of branching processes to model early transmission in an epidemic. An inhomogeneous branching process is derived which allows the study of transmission dynamics early in an epidemic. A generation dependent offspring distribution allows for the branching process to have sub-exponential growth on average. The multi-scale nature of a branching process allows us to utilise both time series of incidence and infection networks. This methodology is applied to data collected during the 2014–2016 Ebola epidemic in West-Africa leading to the inference that transmission grew sub-exponentially in Guinea, Liberia and Sierra Leone. Throughout this thesis, we demonstrate the utility of mechanistic models in epidemiology and how a Bayesian approach to statistical inference is complementary to this.
KeywordsBayesian; statistics; mathematics; stochastic processes; epidemiology; influenza; ebola
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