Vaccination and Variants: retrospective model for the evolution of Covid-19 in Italy

The last year of Covid-19 pandemic has been characterized by the continuous chase between the vaccination campaign and the appearance of new variants that put further obstacles to the possibility of eradicating the virus and returning to normality in a short period. In the present paper we consider a deterministic compartmental model to discuss the evolution of the Covid-19 in Italy as a combined effect of vaccination campaign, new variant spreading, waning immunity and mobility restrictions. We analyze the role that different mechanisms, such as behavioral changes due to variable risk perception, variation of the population mobility, seasonal variability of the virus infectivity, and spreading of new variants have had in shaping the epidemiological curve. The fundamental impact of vaccines in drastically reducing the total increase in infections and deaths is also estimated. This work further underlines the crucial importance of vaccination and adoption of adequate individual protective measures in containing the pandemic.