On real-time calibrated prediction for complex model-based decision support in pandemics: Part 1

Infectious disease models are used to predict the spread and impact of outbreaks of a disease. Like other complex models, they have parameters that need to be calibrated, and structural discrepancies from the reality that they simulate that should be accounted for in calibration and prediction. Whilst Uncertainty Quantification (UQ) techniques have been applied to infectious disease models before, they were not routinely used to inform policymakers in the UK during the COVID-19 pandemic. In this paper, we will argue that during a fast moving pandemic, models and policy are changing on timescales that make traditional UQ methods impractical, if not impossible to implement. We present an alternative formulation to the calibration problem that embeds model discrepancy within the structure of the model, and appropriately assimilates data within the simulation. We then show how UQ can be used to calibrate the model in real-time to produce disease trajectories accounting for parameter uncertainty and model discrepancy. We apply these ideas to an age-structured COVID-19 model for England and demonstrate the types of information it could have produced to feed into policy support prior to the lockdown of March 2020.Author summary: During the COVID-19 pandemic, infectious disease models were used to guide policy decisions under intense time pressure. While parameter calibration and uncertainty quantification (UQ) are essential for interpreting such models, traditional approaches are often too slow or rigid to meet real-time demands. In this paper, we introduce a method for real-time calibration of epidemic models that recognises that all models are simplifications. Our approach embeds model discrepancy (uncertainty due to missing or simplified processes in the model) directly into the simulation. This innovation allows us to handle critical challenges, such as how infection first enters a population (known as the seeding problem), without needing to fix its timing, location, or age distribution in advance. We show how policy-relevant outputs, such as projected hospitalisations or infection trajectories, can be generated quickly while still accounting for key sources of uncertainty. This work was motivated by challenges encountered during real-time policy support for the UK government in the COVID-19 pandemic and is demonstrated on age-structured models for England. It provides a foundation for applying complex models in future outbreaks by using critical but often overlooked uncertainties to improve calibration without sacrificing responsiveness, and supports extensions to models that represent disease spread across regions.