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ORIGINAL RESEARCH article

Front. Phys.
Sec. Social Physics
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1469663
This article is part of the Research Topic Compartmental Models for Social Interactions View all 5 articles

Exponential series approximation of the SIR epidemiological model

Provisionally accepted
Dimiter Prodanov Dimiter Prodanov 1,2*
  • 1 Interuniversity Microelectronics Centre (IMEC), Leuven, Belgium
  • 2 Institute of Information and Communication Technologies (BAS), Sofia, Sofia City, Bulgaria

The final, formatted version of the article will be published soon.

    The SIR (Susceptible-Infected-Recovered) is one of the simplest models for epidemic outbreaks.From a theoretical perspective, the main contribution of this manuscript is the derivation of an infinite exponential series of the model variables. The truncation of the series results in a finite approximate Prony series. This can be interpreted as the emergence of a series of exponential relaxation processes with distinct timescales. The approach is compared to the double-exponential non-linear approximate analytic solution, which exhibits two coupled timescales -a relaxation timescale determined by the ratio of the model time constants and an excitation timescale determined by the population size.

    Keywords: SIR model, Lambert W function, Wright omega function, asymptotic analysis, Incomplete gamma function

    Received: 24 Jul 2024; Accepted: 26 Aug 2024.

    Copyright: © 2024 Prodanov. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Dimiter Prodanov, Interuniversity Microelectronics Centre (IMEC), Leuven, 3001, Belgium

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