Susceptibility-adjusted herd immunity threshold model and potential R ₀ distribution fitting the observed Covid-19 data in Stockholm

The reproduction number, R ₀ , is commonly used, and sometimes misused, in conjunction with the classic Kermack and McKindrick theory based on the assumption of homogeneity, in order to estimate herd immunity threshold (HIT). This provides a crude first estimate of HIT, with more elaborate modelling required to arrive at a more realistic value. Early estimates of HIT for Covid-19 were based on this simplistic homogeneous approach, yielding high HIT values that have since been revised downwards with more sophisticated network modelling taking account of R ₀ heterogeneity and with reference to the low HIT found from serological sampling in Stockholm County. The aim of this paper is to describe a simple model in which host susceptibility is directly linked to the heterogeneous R ₀ distribution, to shed further light on the mechanisms involved and to arrive at a bimodal R ₀ distribution consistent with the Covid-19 HIT observed in Stockholm County.