On real-time calibrated prediction for complex model-based decision support in pandemics: Part 2

Calibration of complex stochastic infectious disease models is challenging. These often have high-dimensional input and output spaces, with the models exhibiting complex, non-linear dynamics. Coupled with a paucity of necessary data, this results in a large number of non-ignorable hidden states that must be handled by the inference routine. Likelihood-based approaches to this missing data problem are very flexible, but challenging to scale, due to having to monitor and update these hidden states. Methods based on simulating the hidden states directly from the model-of-interest have an advantage that they are often more straightforward to code, and thus are easier to implement and adapt in real-time. However, these often require evaluating very large numbers of simulations, rendering them infeasible for many large-scale problems. We present a framework for using emulation-based methods to calibrate a large-scale, stochastic, age-structured, spatial meta-population model of COVID-19 transmission in England and Wales. By embedding a model discrepancy process into the simulation model, and combining this with particle filtering, we show that it is possible to calibrate complex models to high-dimensional data by emulating the log-likelihood surface instead of individual data points. The use of embedded model discrepancy also helps to alleviate other key challenges, such as the introduction of infection across space and time. We conclude with a discussion of major challenges remaining and key areas for future work.Author summary: Mathematical models of infectious disease dynamics are important tools in furthering our understanding of key drivers of epidemic spread, but also in informing the efficacy of potential disease management strategies. During ongoing outbreaks, it is often necessary to develop and fit simulation models to emerging data in real-time, as new information and data emerges. This requires undesirable trade-offs, where increasing model complexity can make the outputs more realistic and useful to policy-makers, but the inference problem far more challenging (and often computationally infeasible within realistic time-frames). In Part 1 we developed a framework for using emulation-based methods (employing fast surrogate models) to calibrate complex epidemic models that overcomes key challenges for real-time development and fitting of complex models using uncertainty quantification methods. In this paper we further develop these approaches and show that they can be scaled to perform well in high-dimensional models, illustrating their utility by successfully calibrating a large-scale, stochastic, age-structured, spatial meta-population model of COVID-19 transmission to data available from 315 spatial regions in England and Wales. We conclude with a discussion about remaining challenges and future directions.