  We study the role of demographic fluctuations in typical endemics as
exemplified by the stochastic SIRS model. The birth-death master equation of
the model is simulated using exact numerics and analysed within the linear
noise approximation. The endemic fixed point is unstable to internal
demographic noise, and leads to sustained oscillations. This is ensured when
the eigenvalues ($\lambda$) of the linearised drift matrix are complex, which
in turn, is possible only if detailed balance is violated. In the oscillatory
state, the phases decorrelate asymptotically, distinguishing such oscillations
from those produced by external periodic forcing. These so-called quasicycles
are of sufficient strength to be detected reliably only when the ratio
$|Im(\lambda)/Re(\lambda)|$ is of order unity. The coherence or regularity of
these oscillations show a maximum as a function of population size, an effect
known variously as stochastic coherence or coherence resonance. We find that
stochastic coherence can be simply understood as resulting from a non-monotonic
variation of $|Im(\lambda)/Re(\lambda)|$ with population size. Thus, within the
linear noise approximation, stochastic coherence can be predicted from a purely
deterministic analysis. The non-normality of the linearised drift matrix,
associated with the violation of detailed balance, leads to enhanced
fluctuations in the population amplitudes.
