  Official freely available data about the number of infected at the finest
possible level of spatial areal aggregation (Italian provinces) are used to
model the spatio-temporal distribution of COVID-19 infections at local level.
Data time horizon ranges from 26 February 20020, which is the date when the
first case not directly connected with China has been discovered in northern
Italy, to 18 March 2020. An endemic-epidemic multivariate time-series
mixed-effects generalized linear model for areal disease counts has been
implemented to understand and predict spatio-temporal diffusion of the
phenomenon. Previous literature has shown that these class of models provide
reliable predictions of infectious diseases in time and space. Three
subcomponents characterize the estimated model. The first is related to the
evolution of the disease over time; the second is characterized by transmission
of the illness among inhabitants of the same province; the third remarks the
effects of spatial neighbourhood and try to capture the contagion effects of
nearby areas. Focusing on the aggregated time-series of the daily counts in
Italy, the contribution of any of the three subcomponents do not dominate on
the others and our predictions are excellent for the whole country, with an
error of 3 per thousand compared to the late available data. At local level,
instead, interesting distinct patterns emerge. In particular, the provinces
first concerned by containment measures are those that are not affected by the
effects of spatial neighbours. On the other hand, for the provinces the are
currently strongly affected by contagions, the component accounting for the
spatial interaction with surrounding areas is prevalent. Moreover, the proposed
model provides good forecasts of the number of infections at local level while
controlling for delayed reporting.
