Exponential series approximation of the SIR epidemiological model - Prodanov, Dimiter (Frontiers in Physics, 2024)
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.