The importance of saturating density dependence for population-level predictions of SARS-CoV-2 resurgence compared with density-independent or linearly density-dependent models, England, 23 March to 31 July 2020

Background Population-level mathematical models of outbreaks typically assume that disease transmission is not impacted by population density (‘frequency-dependent’) or that it increases linearly with density (‘density-dependent’). Aim We sought evidence for the role of population density in SARS-CoV-2 transmission. Methods Using COVID-19-associated mortality data from England, we fitted multiple functional forms linking density with transmission. We projected forwards beyond lockdown to ascertain the consequences of different functional forms on infection resurgence. Results COVID-19-associated mortality data from England show evidence of increasing with population density until a saturating level, after adjusting for local age distribution, deprivation, proportion of ethnic minority population and proportion of key workers among the working population. Projections from a mathematical model that accounts for this observation deviate markedly from the current status quo for SARS-CoV-2 models which either assume linearity between density and transmission (30% of models) or no relationship at all (70%). Respectively, these classical model structures over- and underestimate the delay in infection resurgence following the release of lockdown. Conclusion Identifying saturation points for given populations and including transmission terms that account for this feature will improve model accuracy and utility for the current and future pandemics.