A model shows herd immunity to COVID can be achieved at a population-wide infection rate of ~40%

I pass on the editor's summary and the abstract for a open source article by Britton et al.:  

Heterogeneity and herd immunity

In response to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), some politicians have been keen to exploit the idea of achieving herd immunity. Countering this possibility are estimates derived from work on historical vaccination studies, which suggest that herd immunity may only be achieved at an unacceptable cost of lives. Because human populations are far from homogeneous, Britton et al. show that by introducing age and activity heterogeneities into population models for SARS-CoV-2, herd immunity can be achieved at a population-wide infection rate of ∼40%, considerably lower than previous estimates. This shift is because transmission and immunity are concentrated among the most active members of a population, who are often younger and less vulnerable. If nonpharmaceutical interventions are very strict, no herd immunity is achieved, and infections will then resurge if they are eased too quickly.

Abstract

Despite various levels of preventive measures, in 2020, many countries have suffered severely from the coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Using a model, we show that population heterogeneity can affect disease-induced immunity considerably because the proportion of infected individuals in groups with the highest contact rates is greater than that in groups with low contact rates. We estimate that if R0 = 2.5 in an age-structured community with mixing rates fitted to social activity, then the disease-induced herd immunity level can be ~43%, which is substantially less than the classical herd immunity level of 60% obtained through homogeneous immunization of the population. Our estimates should be interpreted as an illustration of how population heterogeneity affects herd immunity rather than as an exact value or even a best estimate.