Beyond Data-Augmentation: Advancing Bayesian Inference for Stochastic Disease Transmission Models

Background. Over the past three decades, the field of mathematical modelling of communicable diseases has experienced remarkable growth, initially fuelled by the emergence of HIV/AIDS and later by high-profile outbreaks such as Foot and Mouth Disease, SARS, Ebola, and Zika virus. More recently, the COVID-19 pandemic highlighted the critical importance of mathematical and statistical models as fundamental tools for unravelling the dynamics of the spread of infectious diseases, making predictions, quantifying risks, informing public health policy, designing effective control strategies, and assessing existing control measures. However, the increasing complexity of large-scale models, designed to capture real-world behaviours and interactions, presents significant statistical challenges. These models must be carefully calibrated to available data to ensure their reliability. Despite considerable progress made in recent years, fitting complex models to disease outbreak data remains a challenging task. Therefore, there is an urgent need for innovative and efficient computational tools in this area. Aims and Objectives. The overall aim of the proposed research is to create the next generation of tools which can be used for fitting general stochastic Susceptible-Exposed-Infective-Removed (SEIR) epidemic models to infectious disease outbreak data within a Bayesian framework. Our objectives are (i) to develop likelihood approximation methods that can be used to fit general SEIR models with arbitrary infection rates between individuals, (ii) to develop neural posterior estimation methods suitable for robust, efficient and scalable inference for both final outcome and temporal data, (iii) to implement the developed methods using computationally efficient approaches, assess them using simulated data and demonstrate their applicability using real data. Methods. One of the main challenges in fitting stochastic epidemic models to data is that the so-called likelihood of the observed data is almost always intractable, since its derivation involves calculating all the possible ways that the unobserved transmission process resulted in the observed cases of disease (e.g. symptom onset dates). We will exploit the underlying structure of epidemic models to find ways of deriving an approximation to the intractable likelihood which is both accurate enough to be useful in a statistical analysis and relatively easy to compute. We will also capitalise on the recent developments in deep learning and neural networks to approximate posterior distributions based only on simulations/realisations from the model. In order to ground the methods in real-life applications, we will benchmark them against state-of-the-art methods on synthetic and real data. Timelines for delivery. This is a 42-month project involving three work streams each addressing one of the three objectives. Anticipated impact and dissemination. Infectious disease epidemiologists will benefit from having improved tools to analyse outbreak data more efficiently, enabling better understanding of disease dynamics, transmission patterns, and the factors driving pathogen spread. This will support evidence-based recommendations for public health interventions. In addition to dissemination via high-impact scientific and medical journals and conferences, we will produce software and training material to encourage a wider adoption of our developed methods by researchers and practitioners.