  The effects of demographic stochasticity in the long term behaviour of
endemic infectious diseases have been considered for long as a necessary
addition to an underlying deterministic theory. The latter would explain the
regular behaviour of recurrent epidemics, and the former the superimposed noise
of observed incidence patterns. Recently, a stochastic theory based on a
mechanism of resonance with internal noise has shifted the role of
stochasticity closer to the center stage, by showing that the major dynamic
patterns found in the incidence data can be explained as resonant fluctuations,
whose behaviour is largely independent of the amplitude of seasonal forcing,
and by contrast very sensitive to the basic epidemiological parameters. Here we
elaborate on that approach, by adding an ingredient which is missing in
standard epidemic models, the 'mixing network' through which infection may
propagate. We find that spatial correlations have a major effect in the
enhancement of the amplitude and the coherence of the resonant stochastic
fluctuations, providing the ordered patterns of recurrent epidemics, whose
period may differ significantly from that of the small oscillations around the
deterministic equilibrium. We also show that the inclusion of a more realistic,
time correlated, recovery profile instead of exponentially distributed
infectious periods may, even in the random-mixing limit, contribute to the same
effect.
