Data from: The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection

Emerging epidemics and local infection clusters are initially prone to
stochastic effects that can substantially impact the epidemic trajectory.
While numerous studies are devoted to the deterministic regime of an
established epidemic, mathematical descriptions of the initial phase of
epidemic growth are comparatively rarer. Here, we review existing
mathematical results on the epidemic size over time, and derive new
results to elucidate the early dynamics of an infection cluster started by
a single infected individual. We show that the initial growth of epidemics
that eventually take off is accelerated by stochasticity. These results
are critical to improve early cluster detection and control. As an
application, we compute the distribution of the first detection time of an
infected individual in an infection cluster depending on the testing
effort, and estimate that the SARS-CoV-2 variant of concern Alpha detected
in September 2020 first appeared in the United Kingdom early August 2020.
We also compute a minimal testing frequency to detect clusters before they
exceed a given threshold size. These results improve our theoretical
understanding of early epidemics and will be useful for the study and
control of local infectious disease clusters.