Phenomenological description of spread of Covid-19 in Italy: people mobility as main factor controlling propagation of infection cases

Abstract: The spread of the coronavirus (COVID-19), starting in late 2019, has determined in Italy several interventions aimed to prevent saturation of the health system. We have examined the effects of such measures by proposing a mean-field model describing the spread of the infection based on a simple diffusion process where all the observable variables (number of people still positive to the infection, hospitalized and fatalities cases, healed people, and total number of people that has contracted the infection) depend on average parameters, namely diffusion coefficient, infection cross-section, and population density. Although this model is less sophisticated than other models in the literature, it allows us to directly relate the trend of the epidemic statistical information (hospitalized cases, number of fatalities, number of infected people, etc.) to a well defined observable physical quantity: the average number of people that any individual meets per day. The model fits very well the epidemic data, and allows us to strictly relate the time evolution of the number of hospitalized case and fatalities of the outbreak to the change of people mobility, consequent to the implementation of progressive restrictions in Italy, running until the present days (November the 15th, 2020).