Systematic description of COVID-19 pandemic using exact SIR solutions and Gumbel distributions

TL;DR

This study analyzes COVID-19 death data from multiple countries using exact SIR model solutions and Gumbel distributions, revealing that most countries' data fit well with the SIR model with high reproduction numbers.

Contribution

It introduces a parametric solution of the SIR model using proper time and compares it with Gumbel approximations, providing a systematic description of the pandemic's first wave.

Findings

Most countries' death data fit the SIR model well

Estimated basic reproduction numbers range from 3 to 8

Gumbel functions closely approximate SIR solutions

Abstract

An epidemiological study of deaths is carried out in a dozen countries by analyzing the first wave of the COVID-19 pandemic. These countries are among those most affected by the first wave, i.e. where daily-death data series may closely resemble a solution of the basic SIR equations. The SIR equations are solved parametrically using the proper time as parameter. Some general properties of the SIR solutions are studied such as time-scaling and asymmetry. Additionally, we use approximations to the SIR solutions through Gumbel functions, which present a very similar behavior. The parameters of the SIR model and the Gumbel function are extracted from the data and compared for the different countries. It is found that ten of the selected countries are very well described by the solutions of the SIR model, with a basic reproduction number between 3 and 8.