COVID-19 cluster size and transmission rates in schools from crowdsourced case reports

The role of schools in the spread of the COVID-19 pandemic is controversial, with some claiming they are an important driver of the pandemic and others arguing that transmission in schools is negligible. School cluster reports that have been collected in various jurisdictions are a source of data about transmission in schools. These reports consist of the name of a school, a date, and the number of students known to be infected. We provide a simple model for the frequency and size of clusters in this data, based on random arrivals of index cases at schools who then infect their classmates with a highly variable rate, fitting the overdispersion evident in the data. We fit our model to reports from four Canadian provinces, providing estimates of mean and dispersion for cluster size, whilst factoring in imperfect ascertainment. Our parameter estimates are robust to variations in ascertainment fraction. We use these estimates in two ways: i) to explore how uneven the distribution of cases is among different clusters in different jurisdictions (that is, what fraction of cases are in the 20% largest clusters), and ii) to determine the distribution of instantaneous transmission rate β among different index cases. We show how these latter distributions can be used in simulations of school transmission where we explore the effect of different interventions, in the context of highly variable transmission rates.