Computational aspects of the approximate analytic solutions of the SIR model: applications to modelling of COVID-19 outbreaks

The SIR (susceptible–infected–recovered) is one of the simplest models for epidemic outbreaks. The present paper demonstrates the parametric solution of the model in terms of quadratures and derives a double exponential analytical asymptotic solution for the I-variable, which is valid on the entire real line. Moreover, the double exponential 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 parametric solution. A second, refined, asymptotic solution involving exponential gamma kernels was also demonstrated. The approach was applied to the coronavirus disease 2019 (COVID-19) pandemic in six European countries—Belgium, Italy, Sweden, France, Spain and Bulgaria in the period 2020-2021.