Asymptotic analysis of the SIR model and the Gompertz distribution

Abstract

The SIR (Susceptible-Infected-Removed) is one of the simplest models for epidemic outbreaks. The present paper derives a novel, simple, analytical asymptotic solution for the I-variable, which is valid on the entire real line. Connections with the Gompertz and Gumbel distributions are also demonstrated. The approach is applied to the ongoing coronavirus disease 2019 (COVID-19) pandemic in four European countries - Belgium, Italy, Sweden, and Bulgaria. The reported raw incidence data from the outbreaks in 2020-2021 have been fitted using constrained least squares. It is demonstrated that the asymptotic solution can be used successfully for parametric estimation either in stand-alone mode or as a preliminary step in the parametric estimation using numerical inversion of the exact parametric solution.(c) 2022 Elsevier B.V. All rights reserved.