  We explore the inclusion of vaccination in compartmental epidemiological
models concerning the delta and omicron variants of the SARS-CoV-2 virus that
caused the COVID-19 pandemic. We expand on our earlier compartmental-model work
by incorporating vaccinated populations. We present two classes of models that
differ depending on the immunological properties of the variant. The first one
is for the delta variant, where we do not follow the dynamics of the vaccinated
individuals since infections of vaccinated individuals were rare. The second
one for the far more contagious omicron variant incorporates the evolution of
the infections within the vaccinated cohort. We explore comparisons with
available data involving two possible classes of counts, fatalities and
hospitalizations. We present our results for two regions, Andalusia and
Switzerland (including the Principality of Liechtenstein), where the necessary
data are available. In the majority of the considered cases, the models are
found to yield good agreement with the data and have a reasonable predictive
capability beyond their training window, rendering them potentially useful
tools for the interpretation of the COVID-19 and further pandemic waves, and
for the design of intervention strategies during these waves.
