  In this paper we introduce a compartmental epidemic model describing the
transmission of the COVID-19 disease in presence of non-mandatory vaccination.
The model takes into account the hesitancy and refusal of vaccination. To this
aim, we employ the information index, which mimics the idea that individuals
take their decision on vaccination based not only on the present but also on
the past information about the spread of the disease. Theoretical analysis and
simulations show clearly as a voluntary vaccination can certainly reduce the
impact of the disease but it is unable to eliminate it. We also show how the
information-related parameters affect the dynamics of the disease. In
particular, the hesitancy and refusal of vaccination is better contained in
case of large information coverage and small memory characteristic time.
Finally, the possible influence of seasonality is also investigated.
