Frailty variation models for susceptibility and exposure to SARS-CoV-2

Individual variation in susceptibility and exposure is subject to selection by force of infection, accelerating the natural acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as "frailty variation" in demography. Despite this theoretical understanding, public health policies continue to be guided by mathematical models that leave out most of the relevant variation and as a result inflate projected infection burdens. Here we focus on the trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland. We fit models to series of daily deaths and estimate relevant epidemiological parameters, including coefficients of variation which we find in agreement with direct measurements based on published contact surveys. Our estimates are robust to whether the data series encompass one or two pandemic waves. We conclude that herd immunity thresholds are being reached with a larger contribution of vaccination in Scotland than in England, where naturally acquired immunity is higher. These results are relevant to global vaccination policies.