Epidemic modelling: aspects where stochasticity matters

TL;DR

This paper emphasizes the importance of incorporating stochastic elements into epidemic models, especially for accurately estimating outbreak probabilities and growth rates, highlighting the limitations of deterministic models.

Contribution

It demonstrates how stochastic models better capture epidemic dynamics, particularly in early outbreak stages, and discusses implications for estimating key parameters like R0.

Findings

Stochastic models improve outbreak probability predictions.

Random infectious and latent periods affect growth rate estimates.

Early outbreak data sensitivity to distribution assumptions.

Abstract

Epidemic models are always simplifications of real world epidemics. Which real world features to include, and which simplifications to make, depend both on the disease of interest and on the purpose of the modelling. In the present paper we discuss some such purposes for which a \emph{stochastic} model is preferable to a \emph{deterministic} counterpart. The two main examples illustrate the importance of allowing the infectious and latent periods to be random when focus lies on the \emph{probability} of a large epidemic outbreak and/or on the initial \emph{speed}, or growth rate, of the epidemic. A consequence of the latter is that estimation of the basic reproduction number $R_0$ is sensitive to assumptions about the distributions of the infectious and latent periods when using the data from the early stages of an outbreak, which we illustrate with data from the SARS outbreak. Some further examples are also discussed as are some practical consequences related to these stochastic aspects.