Inferring generation-interval distributions from contact-tracing data

Generation intervals, defined as the time between when an individual is infected and when that individual infects another person, link two key quantities that describe an epidemic: the reproductive number, ℛ, and the rate of exponential growth, r. Generation intervals are often measured through contact tracing by identifying who infected whom. We study how observed intervals differ from “intrinsic” intervals that could be estimated by tracing individual-level infectiousness, and identify both spatial and temporal effects, including cen-soring (due to observation time), and the effects of susceptible depletion at various spatial scales. Early in an epidemic, we expect the variation in the observed generation intervals to be mainly driven by the censoring and the population structure near the source of disease spread; therefore, we predict that correcting observed intervals for the effect of temporal censoring but not for spatial effects will provide a spatially informed “effective” generation-interval distribution, which will correctly link r and ℛ. We develop and test statistical methods for temporal corrections of generation intervals, and confirm our prediction using individual-based simulations on an empirical network.