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

Variation in individual susceptibility or frequency of exposure to infection accelerates the rate at which populations acquire immunity by natural infection. Individuals that are more susceptible or more frequently exposed tend to be infected earlier and hence more quickly selected out of the susceptible pool, decelerating the incidence of new infections as the epidemic progresses. Eventually, susceptible numbers become low enough to prevent epidemic growth or, in other words, the herd immunity threshold (HIT) is reached. We have recently proposed a method whereby mathematical models, with gamma distributions of susceptibility or exposure to SARS-CoV-2, are fitted to epidemic curves to estimate coefficients of individual variation among epidemiological parameters of interest. In the initial study we estimated HIT around 25-29% for the original Wuhan virus in England and Scotland. Here we explore the limits of applicability of the method using Spain and Portugal as case studies. Results are robust and consistent with England and Scotland, in the case of Spain, but fail in Portugal due to particularities of the dataset. We describe failures, identify their causes, and propose methodological extensions. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement M.U.F. received funding from Conselho Nacional de Desenvolvimento Cientifico e Tecnologio (CNPq), Brazil. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: NA I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes Datasets are publicly available at the respective national ministry of health websites.