Approximating the epidemic curve

TL;DR

This paper demonstrates that common epidemic models' initial growth and subsequent deterministic susceptibility course stem from a local branching structure, with the deterministic phase derived from the backward process distribution.

Contribution

It shows that epidemic models' key features arise from local branching assumptions and provides a method to determine the deterministic course from the backward process distribution.

Findings

Initial epidemic growth approximated by a branching process

Deterministic susceptibility course derived from backward process

Applicable to various models like Kermack-McKendrick, Reed-Frost, and Volz models

Abstract

Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that are susceptible follows a more or less deterministic course. In this paper, we show that both of these features are consequences of assuming a locally branching structure in the models, and that the deterministic course can itself be determined from the distribution of the limiting random variable associated with the backward, susceptibility branching process. Examples considered include a stochastic version of the Kermack & McKendrick model, the Reed-Frost model, and the Volz configuration model.