Modelling the spread of Covid19 in Italy using a revised version of the SIR model

TL;DR

This paper introduces a modified SIR model incorporating an exponentially decaying reproduction number to accurately predict Covid-19 spread in Italy, successfully forecasting the epidemic peak with high precision.

Contribution

The study develops a revised SIR model with a time-dependent R0, demonstrating improved predictive accuracy for Covid-19 epidemic dynamics in Italy.

Findings

Model reproduces real epidemic behavior with 5% error.

Predicted epidemic peak within 1,000 cases of actual data.

Model effectively forecasts future scenarios based on R0 variations.

Abstract

In this paper, we present a model to predict the spread of the Covid-19 epidemic and apply it to the specific case of Italy. We started from a simple Susceptible, Infected, Recovered (SIR) model and we added the condition that, after a certain time, the basic reproduction number $R_0$ exponentially decays in time, as empirically suggested by world data. Using this model, we were able to reproduce the real behavior of the epidemic with an average error of 5\%. Moreover, we illustrate possible future scenarios, associated to different intervals of $R_0$. This model has been used since the beginning of March 2020, predicting the Italian peak of the epidemic in April 2020 with about 100.000 detected active cases. The real peak of the epidemic happened on the 20th of April 2020, with 108.000 active cases. This result shows that the model had predictive power for the italian case.