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We have further extended our compartmental model describing the spread of the infection in Italy. As in our previous work, the model assumes that the time evolution of the observable quantities (number of people still positive to the infection, hospitalized and fatalities cases, healed people, and total number of people that has contracted the infection) depends on average parameters, namely people diffusion coefficient, infection cross-section, and population density. The model provides information on the tight relationship between the variation of the reported infection cases and a well-defined observable physical quantity: the average number of people that lie within the daily displacement area of any single person. With respect to our previous paper, we have extended the analyses to several regions in Italy, characterized by different levels of restrictions and we have correlated them to the diffusion coefficient. Furthermore, the model now includes self-consistent evaluation of the reproduction index, effect of immunization due to vaccination, and potential impact of virus variants on the dynamical evolution of the outbreak. The model fits the epidemic data in Italy, and allows us to strictly relate the time evolution of the number of hospitalized cases and fatalities to the change of people mobility, vaccination rate, and appearance of an initial concentration of people positives for new variants of the virus. [ABSTRACT FROM AUTHOR]