4.7 Article

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

Journal

NONLINEAR DYNAMICS
Volume 111, Issue 16, Pages 15613-15631

Publisher

SPRINGER
DOI: 10.1007/s11071-023-08656-8

Keywords

SIR model; Lambert W function; Asymptotic analysis; Incomplete gamma function; Gompertz distribution

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This study provides a parametric solution and two exponential analytical asymptotic solutions for the SIR model in epidemic outbreaks, which can be used for estimation of the COVID-19 pandemic in six European countries.
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.

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