Plug-and-play inference for disease dynamics: measles in large and small populations as a case study

Statistical inference for mechanistic models of partially observed dynamic systems is an active area of research. Most existing inference methods place substantial restrictions upon the form of models that can be fitted and hence upon the nature of the scientific hypotheses that can be entertained and the data that can be used to evaluate them. In contrast, the so-called plug-and-play methods require only simulations from a model and are thus free of such restrictions. We show the utility of the plug-and-play approach in the context of an investigation of measles transmission dynamics. Our novel methodology enables us to ask and answer questions that previous analyses have been unable to address. Specifically, we demonstrate that plug-and-play methods permit the development of a modelling and inference framework applicable to data from both large and small populations. We thereby obtain novel insights into the nature of heterogeneity in mixing and comment on the importance of including extra-demographic stochasticity as a means of dealing with environmental stochasticity and model misspecification. Our approach is readily applicable to many other epidemiological and ecological systems

Prediction of Infectious Disease outbreaks based on limited information

The last two decades have seen several large-scale epidemics of international impact, including human, animal and plant epidemics. Policy makers face health challenges that require epidemic predictions based on limited information. There is therefore a pressing need to construct models that allow us to frame all available information to predict an emerging outbreak and to control it in a timely manner. The aim of this thesis is to develop an early-warning modelling approach that can predict emerging disease outbreaks. Based on Bayesian techniques ideally suited to combine information from different sources into a single modelling and estimation framework, I developed a suite of approaches to epidemiological data that can deal with data from different sources and of varying quality. The SEIR model, particle filter algorithm and a number of influenza-related datasets were utilised to examine various models and methodologies to predict influenza outbreaks. The data included a combination of consultations and diagnosed influenza-like illness (ILI) cases for five influenza seasons. I showed that for the pandemic season, different proxies lead to similar behaviour of the effective reproduction number. For influenza datasets, there exists a strong relationship between consultations and diagnosed datasets, especially when considering time-dependent models. Individual parameters for different influenza seasons provided similar values, thereby offering an opportunity to utilise such information in future outbreaks. Moreover, my findings showed that when the temperature drops below 14°C, this triggers the first substantial rise in the number of ILI cases, highlighting that temperature data is an important signal to trigger the start of the influenza epidemic. Further probing was carried out among Maltese citizens and estimates on the under-reporting rate of the seasonal influenza were established. Based on these findings, a new epidemiological model and framework were developed, providing accurate real-time forecasts with a clear early warning signal to the influenza outbreak. This research utilised a combination of novel data sources to predict influenza outbreaks. Such information is beneficial for health authorities to plan health strategies and control epidemics

A dynamic Bayesian Markov model for health economic evaluations of interventions in infectious disease

Background. Health economic evaluations of interventions against infectious diseases are commonly based on the predictions of compartmental models such as ordinary differential equation (ODE) systems and Markov models (MMs). In contrast to standard MMs, ODE systems of infectious diseases are commonly dynamic and account for the effects of herd immunity. This is crucial to prevent overestimation of infection prevalence. Despite their computational effort, ODE systems including whole distributions on model parameters are considered the ``gold standard'' in infectious disease modelling. However, the literature mainly contains ODE-based models which only include a predefined value on each model parameter and thus do not account for parameter uncertainty. As a consequence, probabilistic sensitivity analysis, a crucial component of health economic evaluations, cannot be conducted straightforwardly. Methodology. We present an approach to a dynamic MM under a Bayesian framework. The stochastic MM incorporates a probability distribution on each model parameter. We extend a static MM by incorporating the force of infection into the state allocation algorithm. The corresponding output is based on dynamic changes in population prevalence. In contrast to deterministic ODE-based models including a predefined value for each parameter, probabilistic sensitivity analysis can be conducted straightforwardly. The main motivation for our approach was to conduct a cost-effectiveness analysis of human papillomavirus vaccination. Results. We introduce a case study of a fictional sexually transmitted infection. By means of this example, we show that our methodology produces results which are comparable to the ``gold standard'' of an ODE system in a Bayesian framework. When applied to a cost-effectiveness analysis of human papillomavirus vaccination, our method indicates that universal vaccination (including both sexes) is cost-effective. A comparison of universal to female-only vaccination and cervical screening-only results in an Incremental Cost-Effectiveness Ratio (ICER) of €11,600 and €1,500, respectively. Conclusions. The dynamic Bayesian MM is suitable to include a high number of states and age cohorts, which are for example required in conclusive human papillomavirus modelling. In contrast to deterministic ODE systems, the setting is fully probabilistic at manageable computational effort