The approximately universal shapes of epidemic curves in the Susceptible-Exposed-Infectious-Recovered (SEIR) model

TL;DR

This paper demonstrates that epidemic curves in the SEIR model share a universal shape with the SIR model, scaled by a factor related to incubation and infectious periods, revealing a universal timescale dependent on key parameters.

Contribution

It generalizes an existing semi-analytical solution to the SEIR model, showing the universal shape of epidemic curves across different parameter settings.

Findings

SEIR curves resemble SIR curves with a time stretch factor

The stretch factor depends on incubation and infectious periods

A universal timescale is identified based on basic reproduction number

Abstract

Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the approach of Harko et al. (2014) is generalised to obtain an approximate semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) model. The SEIR model curves have nearly the same shapes as the SIR ones, but with a stretch factor applied to them across time that is related to the ratio of the incubation to infectious periods. This finding implies an approximate characteristic timescale, scaled by this stretch factor, that is universal to all SEIR models, which only depends on the basic reproduction number and initial fraction of the population that is infectious.