  We study a fast-slow version of an SIRS epidemiological model on homogeneous
graphs, obtained through the application of the moment closure method. We use
GSPT to study the model, taking into account that the infection period is much
shorter than the average duration of immunity. We show that the dynamics occurs
through a sequence of fast and slow flows, that can be described through
2-dimensional maps that, under some assumptions, can be approximated as
1-dimensional maps. Using this method, together with numerical bifurcation
tools, we show that the model can give rise to periodic solutions, differently
from the corresponding model based on homogeneous mixing.
