  The main aim of the work is to present a general class of two time scales
discrete-time epidemic models. In the proposed framework the disease dynamics
is considered to act on a slower time scale than a second different process
that could represent movements between spatial locations, changes of individual
activities or behaviours, or others. To include a sufficiently general disease
model, we first build up from first principles a discrete-time
Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS) model and
characterize the eradication or endemicity of the disease with the help of its
basic reproduction number R0. Then, we propose a general full model that
includes sequentially the two processes at different time scales, and proceed
to its analysis through a reduced model. The basic reproduction number R0 of
the reduced system gives a good approximation of the R0 of the full model since
it serves at analyzing its asymptotic behaviour. As an illustration of the
proposed general framework, it is shown that there exist conditions under which
a locally endemic disease, considering isolated patches in a metapopulation,
can be eradicated globally by establishing the appropriate movements between
patches.
