Modeling provincial Covid-19 epidemic data in Italy using an adjusted time-dependent SIRD model
The outbreak of the Covid-19 epidemics in early 2020 has caused an unprecedented effort of the scientific community to produce models that could monitor and predict the evolution of the epidemics in a reliable way, also to advice governments to take actions which could mitigate the burden of hospitals to treat the affected patients, and reducing the mortality rate of the infection.
The first reported Italian case of Covid-19 dates back to February 20th, 2020 in the city of Codogno, southern Lombardy, and the epidemics spread particularly in Italian northern regions, that is, those most commercially connected with China, where the epidemics had its origin. The Italian government took subsequent measures to contain the epidemics, ending soon with a full national lockdown on March 11th, 2020, to drastically reduce the mobility of citizens and the consequent infectious contacts.
We decided to focus on the modelling of the epidemics in Italian provinces (i.e. at EU NUTS-3 level), rather than in Italian regions (i.e. at EU NUTS-2 level). This choice was dictated by the fact that the Covid-19 outbreak in Italy has been not homogeneously spread within regions, with many differences from province to province in the same region.
We considered a model consisting of 4 compartments: susceptible (S), infected (I), recovered (R) and died (D), that were the only compartments for which we could find available data at NUTS-3 level in Italy.
In the case of SARS-Cov-2 virus, it was proven that the infection has an incubation period of about 5 days and that a significant percentage of the infected people are asymptomatic, thus actually more compartments should and have been considered both in deterministic and stochastic models. Unfortunately the data unavailability at NUTS-3 level would cause problems in the parameters identification. Furthermore we decided to keep the model as simple as possible in order to make it more accountable and, at the same time, robust to the variation in time of the parameters.
The parameters of the epidemics are actually evolving in time. In fact, the rate of infection depends implicitly on the limitation of the mobility of the citizens; on the measures of protection of the healthcare personnel and of the workers who kept on doing jobs which were considered essential services to the community; on the number of swab tests performed locally to detect the infected subjects in order to put them in strict quarantine. Also the recovery rate and the death rate are changing in time and in space because of the different burden of the local healthcare systems and the new insights in the pulmonary illness caused by the SARS-Cov-2 virus and its possible pharmacological and medical treatment. We thus studied a SIRD model whose parameters are evolving in time, and able to automatically adapt to the factors which are implicitly causing their changes. This makes our model able to predict with a good reliability the short term evolution of the epidemics, in particular in absence of sudden big changes of the population behavior or the health policy.
For further details see:
Luisa Ferrari, Giuseppe Gerardi, Giancarlo Manzi, Alessandra Micheletti, Federica Nicolussi, Elia Biganzoli, Silvia Salini, Modelling provincial Covid-19 epidemic data in Italy using an adjusted time-dependent SIRD model