Duration of Transients in Outbreaks: When can Infectiousness be Estimated?

TL;DR

This paper analyzes the transient dynamics of COVID-19 outbreaks using SEIR models with contact matrices, identifying when the growth rate stabilizes enough to estimate transmission potential in realistic scenarios.

Contribution

It provides a quantitative estimate of the transient period in SEIR models, guiding data collection timing for outbreak analysis and extending findings to airborne diseases.

Findings

Transients typically last around 3 weeks in realistic outbreaks.

Growth rate estimates become reliable after about 4-5 incubation periods.

Results are applicable to other airborne diseases in well-mixed populations.

Abstract

We investigate sub-leading orders of the classic SEIR-model using contact matrices from modeling of the Omicron and Delta variants of COVID-19 in Denmark. The goal of this is to illustrate when the growth rate, and by extension the infection transmission potential (basic or initial reproduction number), can be estimated in a new outbreak, e.g. after introduction of a new variant of a virus. In particular, we look at the time scale on which this happens in a realistic outbreak to guide future data collection. We find that as long as susceptible depletion is a minor effect, the transients are gone within around 3 weeks corresponding to about 4-5 times the incubation time. We also argue that this result generalizes to other airborne diseases in a fully mixed population.