Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics

Abstract

As severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spreads, the susceptible subpopulation declines causing the rate at which new infections occur to slow down. Variation in individual susceptibility or exposure to infection exacerbates this effect. Individuals that are more susceptible or more exposed tend to be infected and removed from the susceptible subpopulation earlier. This selective depletion of susceptibles intensifies the deceleration in incidence. Eventually, susceptible numbers become low enough to prevent epidemic growth or, in other words, the herd immunity threshold is reached. Here we fit epidemiological models with inbuilt distributions of susceptibility or exposure to SARS-CoV-2 outbreaks to estimate basic reproduction numbers (R_0) alongside coefficients of individual variation (CV) and the effects of containment strategies. Herd immunity thresholds are then calculated as 1-(1⁄R_0 )^(1⁄((1+〖CV〗^2 ) )) or 1-(1⁄R_0 )^(1⁄((1+〖2CV〗^2 ) )), depending on whether variation is on susceptibility or exposure. Our inferences result in herd immunity thresholds around 10-20%, considerably lower than the minimum coverage needed to interrupt transmission by random vaccination, which for R_0 higher than 2.5 is estimated above 60%. We emphasize that the classical formula, 1-1⁄R_0 , remains applicable to describe herd immunity thresholds for random vaccination, but not for immunity induced by infection which is naturally selective. These findings have profound consequences for the governance of the current pandemic given that some populations may be close to achieving herd immunity despite being under more or less strict social distancing measures.

Lockdown Effects on Sars-CoV-2 Transmission – The evidence from Northern Jutland

“…Early computer modelling indicated that mandated lockdown would be highly effective and prevent hundreds of thousands of deaths. [4] However, the homogenous models used to produce counterfactual curves have been criticized in many papers, since heterogeneity in susceptibility, activity, infectivity, and compliance all tend to flatten curves by themselves relative to counterfactual homogeneous populations [6]- [8], [10], [12]. To the extent that test-driven infection control or voluntary compliance do not fully explain our data, our results are consistent with this criticism and with country-comparison studies showing smaller direct effects of full lockdown itself [16].…”

“…[28] Our results (and most of the above epidemiological retrospective studies, in fact) are at odds with some modelling studies perhaps best illustrated by the study of Flaxman et al [4] In addition to other points raised [29], these models lack the heterogeneity of real populations (the fact that most transmission occurs in a minority of the population, "superspreading", etc. ), which substantially reduces transmission and (transient) herd immunity thresholds [6]- [12]. Thus homogeneous models substantially overestimate the size of counterfactual curves and therefore, effects of NPIs.…”

“…They need to include large ensembles of countries, since there are enough few-country comparisons to favour any desired hypothesis. Erroneous conclusions are risked in particular near the tipping point of a curve partly shaped by confounders that affect natural heterogeneous transmission and susceptibility and thus curve structure [6]- [12], including population age and health status, which in some cases appear to matter more than NPIs. [13]- [16] Even when NPIs appear effective, the voluntary counterfactual to mandates (how the curve would have looked upon recommendation rather than mandate) is not easily identified.…”

Is Herd Immunity Against SARS-CoV-2 a Silver Lining?

“…However, it remains to be noted that the estimate of the proposed threshold is only theoretical with the assumptions of a homogenous population and presence of uniform sterilizing immunity in the recovered patients. Mathematical modeling studies have shown that disease-induced herd immunity threshold would be substantially lower than the values calculated by conventional formula due to the population heterogeneity (16,17).…”

Impact of pre-existing T cell immunity to SARS-CoV-2 in uninfected individuals with COVID-19 mortality in different countries

“…Prevalence of the pandemic was calculated as numbers of the reported COVID-19 cases normalized per million population.Observations reported in this contribution indicate that pre-existing cross-reactive against SARS-CoV-2 T cells may contribute to the innate herd immunity against COVID-19 and affect populations' susceptibility to the infection. Therefore, if pre-existing cross-reactive against SARS-CoV-2 T cells are significant contributors to populations' herd immunity, the herd immunity threshold required to effectively stop the pandemic can be reduced from 60% of a population getting infected down to as low as 10% based on an R0 of 2.5 (the average number of secondary cases generated by an infectious individual among susceptible people) and achieved depending on the prevalence, quantity, and quality of pre-existing immunity among uninfected people(9)(10)(11). Based on these considerations, it seems likely that the upcoming implementation of even moderately efficient vaccination programs would facilitate the rapid attainment of the desirable herd immunity levels.…”