Uncertainty and error in SARS-CoV-2 epidemiological parameters inferred from population-level epidemic models. (7th February 2023) - Whittaker, Dominic G.; Herrera-Reyes, Alejandra D.; Hendrix, Maurice; Owen, Markus R.; Band, Leah R.; Mirams, Gary R.; Bolton, Kirsty J.; Preston, Simon P.
Abstract: During the SARS-CoV-2 pandemic, epidemic models have been central to policy-making. Public health responses have been shaped by model-based projections and inferences, especially related to the impact of various non-pharmaceutical interventions. Accompanying this has been increased scrutiny over model performance, model assumptions, and the way that uncertainty is incorporated and presented. Here we consider a population-level model, focusing on how distributions representing host infectiousness and the infection-to-death times are modelled, and particularly on the impact of inferred epidemic characteristics if these distributions are mis-specified. We introduce an S I R -type model with the infected population structured by 'infected age', i.e. the number of days since first being infected, a formulation that enables distributions to be incorporated that are consistent with clinical data. We show that inference based on simpler models without infected age, which implicitly mis-specify these distributions, leads to substantial errors in inferred quantities relevant to policy-making, such as the reproduction number and the impact of interventions. We consider uncertainty quantification via a Bayesian approach, implementing this for both synthetic and real data focusing on UK data in the period 15 Feb–14 Jul 2020, and emphasising circumstances where it is misleading to neglect uncertainty. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". Highlights: Simple models of SARS-CoV-2 transmission can describe death data in early 2020. A drop in mixing intensity, and not herd immunity, explains the epidemic decline. Mis-specifying delays to host outcomes yields misleading estimates for R. Models structured by infected-age can capture realistic delays and their uncertainty. Bayesian uncertainty quantification can be misleading if there is model error.