  In this work, using a detailed dataset furnished by National Health
Authorities concerning the Province of Pavia (Lombardy, Italy), we propose to
determine the essential features of the ongoing COVID-19 pandemic in term of
contact dynamics. Our contribution is devoted to provide a possible planning of
the needs of medical infrastructures in the Pavia Province and to suggest
different scenarios about the vaccination campaign which possibly help in
reducing the fatalities and/or reducing the number of infected in the
population. The proposed research combines a new mathematical description of
the spread of an infectious diseases which takes into account both age and
average daily social contacts with a detailed analysis of the dataset of all
traced infected individuals in the Province of Pavia. These information are
used to develop a data-driven model in which calibration and feeding of the
model are extensively used. The epidemiological evolution is obtained by
relying on an approach based on statical mechanics. This leads to study the
evolution over time of a system of probability distributions characterizing the
age and social contacts of the population. One of the main outcomes shows that,
as expected, the spread of the disease is closely related to the mean number of
contacts of individuals. The model permits to forecast thanks to an uncertainty
quantification approach and in the short time horizon, the average number and
the confidence bands of expected hospitalized classified by age and to test
different options for an effective vaccination campaign with age-decreasing
priority.
