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Numerical Simulations of a Modified SIR Model Fitting Statistical Datafor COVID19

We consider a system of ordinary differential equations obtained by modifying the classical SIR modelin epidemiology in order to account for the particular features of COVID­19 and the structure of the availablestatistical data. Its main feature is that the infectious state is being split in two different stages. In the first one,which lasts a few days after being infected, the individuals are considered to be contagious and able to spreadfurther the disease. After this, the individuals are considered to be isolated and this second stage lasts until eitherrecovery or death is reported. The parameters of the model are fitted for several countries (Germany, Italy, Spain,Russia, USA, Romania) such that the solution matches the known number of new cases, active cases, recoveriesand deaths. The values of these parameters give insight regarding the evolution of the pandemy and can revealdifferent policies and approaches in reporting the official data. For example one of them can indicate that in certaincountries a substantial amount of cases were reported only post­mortem. The variation across several countries ofanother parameter, which models the average convalescence time (the duration of the second stage of the infectiousstate), points to the fact that the recoveries are reported at different rates, in some cases with significant delays.Since it can be assumed that this is only a matter of reporting, we also perform additional simulations for thesecountries by taking the average convalescence time the value of Germany, which is the smallest within the wholerange. The conclusion is that under this assumption, the evolution of the active cases for example in Italy andSpain, is not significantly different to that in Germany, the comparison being based on the fact that these countriesshowed a similar number of cases within the considered period.