Integro-differential approach for modeling the COVID-19 dynamics - Impact of confinement measures in Italy.

The COVID-19 pandemic has overwhelmed the life and security of most of the world countries, and especially of the Western countries, without similar experiences in the recent past. In a first phase, the response of health systems and governments was disorganized, but then incisive, also driven by the fear of a new and dramatic phenomenon. In the second phase, several governments, including Italy, accepted the doctrine of "coexistence with the virus" by putting into practice a series of containment measures aimed at limiting the dramatic sanitary consequences while not jeopardizing the economic and social stability of the country. Here, we present a new mathematical approach to modeling the COVID-19 dynamics that accounts for typical evolution parameters (i.e., virus variants, vaccinations, containment measurements). Reproducing the COVID-19 epidemic spread is an extremely challenging task due to the low reliability of the available data, the lack of recurrent patterns, and the considerable amount and variability of the involved parameters. However, the adoption of fairly uniform criteria among the Italian regions enabled to test and optimize the model in various conditions leading to robust and interesting results. Although the regional variability is quite large and difficult to predict, we have retrospectively obtained reliable indications on which measures were the most appropriate to limit the transmissibility coefficients within detectable ranges for all the regions. To complicate matters further, the rapid spread of the English variant has upset contexts where the propagation of contagion was close to equilibrium conditions, decreeing success or failure of a certain measure. Finally, we assessed the effectiveness of the zone assignment criteria, highlighting how the reactivity of the measures plays a fundamental role in limiting the spread of the infection and thus the total number of deaths, the most important factor in assessing the success of epidemic management.