Open AccessThe stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection
Author(s) -
Peter Czuppon,
Emmanuel Schertzer,
François Blanquart,
Florence Débarre
Publication year - 2021
Publication title -
journal of the royal society interface
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.655
H-Index - 139
eISSN - 1742-5689
pISSN - 1742-5662
DOI - 10.1098/rsif.2021.0575
Subject(s) - cluster (spacecraft) , cluster size , epidemic model , dynamics (music) , infectious disease (medical specialty) , statistics , statistical physics , biology , econometrics , computer science , mathematics , demography , physics , disease , medicine , population , molecular dynamics , pathology , quantum mechanics , sociology , acoustics , programming language
Emerging epidemics and local infection clusters are initially prone to stochastic effects that can substantially impact the early 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 size of the epidemic 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. As an application, we compute the distribution of the first detection time of an infected individual in an infection cluster depending on testing effort, and estimate that the SARS-CoV-2 variant of concern Alpha detected in September 2020 first appeared in the UK 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.