  Although previous infection and vaccination provide protection against
SARS-CoV-2 infection, both reinfection and breakthrough infection are possible
events whose occurrence would increase with time after first exposure to the
antigen and with the emergence of new variants of the virus. Periodic
vaccination could counteract this decline in protection. In the present work,
our aim was to develop and explore a model of SARS-CoV-2 spread with
vaccination, reinfection and breakthrough infection. A modified deterministic
SIS (Susceptible-Infected-Susceptible) model represented by a system of
differential equations was designed. As in any SIS model, the population was
divided into susceptible and infected individuals. But in our design,
susceptible individuals were, in turn, grouped into three consecutive
categories whose susceptibility increases with time after infection or
vaccination. The model was studied by means of computer simulations, which were
analysed qualitatively. The results obtained show that the prevalence, after
oscillating between peaks and valleys, reaches a plateau phase. Moreover, as
might be expected, the magnitude of the peaks and plateaus increases as the
infection rate rises, the vaccination rate decreases and the rate of decay of
protection conferred by vaccination or previous infection increases. Therefore,
the present study suggests that, at least under certain conditions, the spread
of SARS-CoV-2, although it could experience fluctuations, would finally evolve
into an endemic form, with a more or less stable prevalence that would depend
on the levels of infection and vaccination, and on the kinetics of
post-infection and post-vaccination protection. However, it should be kept in
mind that our development is a theoretical scheme with many limitations. For
this reason, its predictions should be considered with great care.
