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

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Abstract

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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Data availability

The COVID datasets were downloaded from ECDC using https://opendata.ecdc.europa.eu/covid19/casedistribution/csv. The analysis pertains to the version from 14 Dec 2020, which covers the period 1 Jan 2020–14 Dec 2021. A second dataset was downloaded on 15 Sept 2021. Inspection of the dataset demonstrated that the new data started from 1 March 2021 and covers the 31 countries from the European Economic Area (EEA).

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Authors and Affiliations

  1. Environment, Health and Safety, IMEC, Kapeldreef, 75, 3001,, Leuven, Belgium

    Dimiter Prodanov

  2. ITSDP, IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Dimiter Prodanov

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  1. Dimiter Prodanov
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Reference implementation in the Computer Algebra System Maxima has been developed, and the code is available through the Zenodo repository [27].

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Prodanov, D. Computational aspects of the approximate analytic solutions of the SIR model: applications to modelling of COVID-19 outbreaks. Nonlinear Dyn 111, 15613–15631 (2023). https://doi.org/10.1007/s11071-023-08656-8

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