Asymptotic analysis of the SIR model. Applications to COVID-19 modelling

The SIR (Susceptible-Infected-Removed) model can be very useful in modelling epidemic outbreaks. The present paper derives the parametric solution of the model in terms of quadratures. The paper demonstrates a simple analytical asymptotic solution for the I-variable, which is valid on the entire real line. Moreover, the 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. The approach is applied to the ongoing coronavirus disease 2019 (COVID-19) pandemic in three European countries --Belgium, Italy and Sweden.