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We have further extended our compartmental model describing the spread of theinfection in Italy. The model is based on the assumption that the timeevolution of all of the observable quantities (number of people still positiveto the infection, hospitalized and fatalities cases, healed people, and totalnumber of people that has contracted the infection) depend on averageparameters, namely people diffusion coefficient, infection cross-section, andpopulation density. The model provides precious information on the tightrelationship between the variation of the reported infection cases and a welldefined observable physical quantity: the average number of people that liewithin the daily displacement area of any single person. The extension of themodel now includes self-consistent evaluation of the reproduction index, effectof immunization due to vaccination, and potential impact of virus variants onthe dynamical evolution of the outbreak. The model fits very well the epidemicdata, and allows us to strictly relate the time evolution of the number ofhospitalized case and fatalities to the change of people mobility, vaccinationrate, and appearance of an initial concentration of people positives for newvariants of the virus.

Simulation of the impact of people mobility, vaccination rate, and virus variants on the evolution of Covid-19 outbreak