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

Author:

Bertoin JeanORCID

Abstract

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

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference19 articles.

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5. [8] Iksanov, A. , Kolesko, K. and Meiners, M. (2021). Asymptotic fluctuations in supercritical Crump–Mode–Jagers processes. Available at arXiv:2109.00867.

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