A model for an epidemic with contact tracing and cluster isolation, and a detection paradox

Abstract We determine the distributions of some random variables related to a simple model an epidemic with contact tracing and cluster isolation. This enables us apply general limit theorems for super-critical Crump–Mode–Jagers branching processes. Notably, we compute explicitly asymptotic proportion isolated clusters given size amongst all clusters, conditionally on survival epidemic. Somewhat surprisingly, latter differs from distribution typical at time its detection, explain reasons behind this seeming paradox.