A deterministic compartmental model for the transition between variants in the spread of Covid-19 in Italy

We propose a deterministic epidemic model to describe the transition between two variants of the same virus, through the combination of a series of realistic mechanisms such as par- tial cross immunity, waning immunity for vaccinated individuals and a novel data-based algorithm to describe the average immunological status of the population. The model is vali- dated on the evolution of Covid-19 in Italy, during the period in which the transition between Delta and Omicron variant occurred, with very satisfactory agreement with the experimental data. According to our model, if the vaccine efficacy had been equal against Delta and Omi- cron variant infections, the transition would have been smoothed and the epidemic would have gone extinct. This circumstance confirms the fundamental role of vaccines in combat- ing the epidemic, and the importance of identifying vaccines capable of intercepting new variants.