AUTHOR=Prodanov Dimiter 

TITLE=Exponential series approximation of the SIR epidemiological model

JOURNAL=Frontiers in Physics

VOLUME=Volume 12 - 2024

YEAR=2024

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2024.1469663

DOI=10.3389/fphy.2024.1469663

ISSN=2296-424X

ABSTRACT=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.