Estimation of COVID-19 dynamics "on a back-of-envelope": Does the simplest SIR model provide quantitative parameters and predictions?

Abstract

Basing on existence of the mathematically sequential reduction of the three-compartmental (Susceptible-Infected-Recovered/Removed) model to the Verhulst (logistic) equation with the parameters determined by the basic characteristic of epidemic process, this model is tested in application to the recent data on COVID-19 outbreak reported by the European Centre for Disease Prevention and Control. It is shown that such a simple model adequately reproduces the epidemic dynamics not only qualitatively but for a number of countries quantitatively with a high degree of correlation that allows to use it for predictive estimations. In addition, some features of SIR model are discussed in the context, how its parameters and conditions reflect measures attempted for the disease growth prevention that is also clearly indicated by deviations from such model solutions.

Keywords: Compartmental epidemic model; Covid-19; Logistic regression; SIR model.

Fig. 1

The comparison of COVID-19 outbreak in China (markers) and its fitting with the SIR model (solid line) reduced to the logistic equation with respect to ΣI (left subpanel) and other characteristics: daily I (rate, middle panel), and the Fisher-Pry representation of the logistic growth, where $F=\Sigma I/K$.

Fig. 2

Series of plots, which demonstrate logistic curve fittings (solid parts of curves) and predictions(dashed parts) using the data (markers) registered for different time intervals from the outbreak’s beginning (80, 85, 90, and 95 days since 31/12/2019, day 0). The yellow filled areas denote uncertainty ranges obtained via the Monte Carlo simulations. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3

The Fisher-Pry plots for different countries based on the data available to April 3, 2020 (markers). The solid and dashed line show their fitting and forecast, respectively; the yellow area covers the uncertainty range. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)