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.