Observing the epidemiological SIR model on COVID-19 pandemic data

Abstract

This article shows that in the period January 22-June 04, 2020, the combined  data set of cumulative  recoveries and deaths from the current coronavirus COVID-19 pandemic falls on the Kermack and McKendrick approximated solution of the epidemiological {\sir} contagious
disease model. Then, as an original contribution of this work, based on the knowledge of
the infectious period of any epidemic, a methodology is presented that helps to find numerical solutions of the full {\sir} model that falls on the observed data of the epidemic in case it could be described by the {\sir} model. The methodology is first illustrated by finding a solution of the {\sir} model that falls on the epidemic data of the Bombay plague of 1905-06 analyzed by Kermack and McKendrick. After that, the methodology is applied on analyzing the previously considered coronavirus COVID-19 pandemic data set. Moreover,  since the Kermack and McKendrick approximated solution of the {\sir} model comes from solving a Riccati type differential equation, commonly found when studying (in introductory physics courses) the vertical motion of objects on a resistive medium, enough details are given in the article so the epidemiological {\sir} model can be used as an additional example for enhancing and enriching the undergraduate curriculum Physics courses for Biology, Life Sciences, Medicine and/or Computational Modeling.