  The interplay between the virus, infected cells and the immune responses to
SARS-CoV-2 is still under debate. Extending the basic model of viral dynamics
we propose here a formal approach to describe the neutralizing versus weakly
(or non-)neutralizing scenarios and compare with the possible effects of
antibody-dependent enhancement (ADE). The theoretical model is consistent with
data available from the literature; we show that weakly neutralizing antibodies
or ADE can both give rise to either final virus clearance or disease
progression, but the immuno-dynamic is different in each case. Given that a
significant part of the world population is already naturally immunized or
vaccinated, we also discuss the implications on secondary infections infections
following vaccination or in presence of immune system dysfunctions.
