Analytical parameter estimation of the SIR epidemic model. Applications to the COVID-19 pandemic

TL;DR

This paper derives an explicit analytical solution for the SIR epidemic model involving a new special function, and introduces numerical methods for parameter estimation using COVID-19 data.

Contribution

It provides the first explicit solution to the SIR model involving a new special function and develops algorithms for estimating model parameters from observed epidemic data.

Findings

Explicit solution involves a new transcendental function.

Numerical routines successfully estimate parameters from COVID-19 data.

Applicable to multiple European countries during early 2020.

Abstract

The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modeling and forecasting. The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the community to derive an explicit solution. The present work demonstrates that this is a non-trivial task. Notably, it is proven that the explicit solution of the model requires the introduction of a new transcendental special function, related to the Wright's Omega function. The present manuscript reports new analytical results and numerical routines suitable for parametric estimation of the SIR model. The manuscript introduces iterative algorithms approximating the incidence variable, which allows for estimation of the model parameters from the numbers of observed cases. The numerical approach is exemplified with data from the European Centre for Disease Prevention and Control (ECDC) for several European countries in the period Jan 2020 -- Jun 2020.