The SIR model towards the data: One year of Covid-19 pandemic in Italy case study and plausible “real” numbers

In this work, the SIR epidemiological model is reformulated so to highlight theimportanteffective reproduction number, as well as to account for thegeneration time,theinverse of theincidence rate,andtheinfectious period(orremoval period), the inverse oftheremoval rate. The aim is to check whether the relationships the model poses among thevarious observables are actually found in the data. The study case of the second through thethird wave of the Covid-19 pandemic in Italy is taken. Given its scale invariance, initiallythe model is tested with reference to the curve of swab-confirmed infectious individualsonly. It is found to match the data, if the curve of theremoved(that is healed or deceased)individuals is assumed underestimated by a factor of about 3 together with other relatedcurves. Contextually, thegeneration timeand theremoval period,aswellastheeffectivereproduction number, are obtained fitting the SIR equations to the data; the outcomes proveto be in good agreement with those of other works. Then, using knowledge of the proportionof Covid-19 transmissions likely occurring from individuals who didn’t develop symptoms,thus mainly undetected, an estimate of thereal numbersof the epidemic is obtained, lookingalso in good agreement with results from other, completely different works. The line of thiswork is new, and the procedures, computationally really inexpensive, can be applied to anyother national or regional case besides Italy’s study case here.