  The ubiquity of oscillations in epidemics presents a long standing challenge
for the formulation of epidemic models. Whether they are external and
seasonally driven, or arise from the intrinsic dynamics is an open problem. It
is known that fixed time delays destabilize the steady state solution of the
standard SIRS model, giving rise to stable oscillations for certain parameters
values. In this contribution, starting from the classical SIRS model, we make a
general treatment of the recovery and loss of immunity terms. We present
oscillation diagrams (amplitude and period) in terms of the parameters of the
model, showing how oscillations can be destabilized by the shape of the
distributions of the two characteristic (infectious and immune) times. The
formulation is made in terms of delay equation which are both numerical
integrated and linearized. Results from simulation are included showing where
they support the linear analysis and explaining why not where they do not.
Considerations and comparison with real diseases are presented along.
