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

TL;DR

This paper analyzes the stochastic early dynamics of epidemics, focusing on initial growth, detection probability, and cluster size, providing new mathematical insights to improve early detection and control strategies.

Contribution

It derives new mathematical results on early epidemic growth, detection times, and testing strategies, enhancing understanding of initial epidemic phases compared to prior deterministic models.

Findings

Stochasticity accelerates initial epidemic growth.

Distribution of first detection time depends on testing effort.

Minimal testing frequency can be estimated to detect clusters early.

Abstract

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.