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.

Assessing the impact of data-driven limitations on tracing and forecasting the outbreak dynamics of COVID-19.

The availability of the epidemiological data strongly affects the reliability of several mathematical models in tracing and forecasting COVID-19 pandemic, hampering a fair assessment of their relative performance. The marked difference between the lethality of the virus when comparing the first and second waves is an evident sign of the poor reliability of the data, also related to the variability over time in the number of performed swabs. During the early epidemic stage, swabs were made only to patients with severe symptoms taken to hospital or intensive care unit. Thus, asymptomatic people, not seeking medical assistance, remained undetected. Conversely, during the second wave of infection, total infectives included also a percentage of detected asymptomatic infectives, being tested due to close contacts with swab positives and thus registered by the health system. Here, we compared the outcomes of two SIR-type models (the standard SIR model and the A-SIR model that explicitly considers asymptomatic infectives) in reproducing the COVID-19 epidemic dynamic in Italy, Spain, Germany, and France during the first two infection waves, simulated separately. We found that the A-SIR model overcame the SIR model in simulating the first wave, whereas these discrepancies are reduced in simulating the second wave, when the accuracy of the epidemiological data is considerably higher. These results indicate that increasing the complexity of the model is useless and unnecessarily wasteful if not supported by an increased quality of the available data.