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Using the SIR (Susceptible-Infected-Recovered) model, an epidemiological
model based on three differential equations (see
http://www.public.asu.edu/~hnesse/classes/sir.html), it is possible to
predict in a reasonable manner the evolution of the Coronavirus
infection in Italy. I solved the differential equations and I have found
realistic parameters to interpret the present situation and to give
possible predictions for the future. Moreover, I also improved the
standard SIR model, evolving the probability to be infected in time, in
order to account for the quarantine and other possible restrictions.
Following the behavior of the present data, the result suggests that a
peak will be reached at the end of March / beginning of April. At the
day of the peak order 10^5 people might be infected and 10^4 might need
to be hospitalized. At the end of the pandemic roughly half a million of
Italian are expected to have been infected (2/3 of them without showing
symptoms). This scenario would result in a number of death cases between
20.000 and 30.000.

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