  A family of discrete non-autonomous SIRVS models with general incidence is
obtained from a continuous family of models by applying Mickens non-standard
discretization method. Conditions for the permanence and extinction of the
disease and the stability of disease-free solutions are determined. The
consistency of those discrete models with the corresponding continuous model is
discussed: if the time step is sufficiently small, when we have extinction
(respectively permanence) for the continuous model we also have extinction
(respectively permanence) for the corresponding discrete model. Some numerical
simulations are carried out to compare the different possible discretizations
of our continuous model using real data.
