  The effect of demographic stochasticity, in the form of Gaussian white noise,
in a predator-prey model with one fast and two slow variables is studied. We
derive the stochastic differential equations (SDEs) from a discrete model. For
suitable parameter values, the deterministic drift part of the model admits a
folded node singularity and exhibits a singular Hopf bifurcation. We focus on
the parameter regime near the Hopf bifurcation, where small amplitude
oscillations exist as stable dynamics in the absence of noise. In this regime,
the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which
capture the intermediate dynamics between two cycles of population outbreaks.
We perform numerical simulations to calculate the distribution of the random
number of small oscillations between successive spikes for varying noise
intensities and distance to the Hopf bifurcation. We also study the effect of
noise on a suitable Poincar\'e map. Finally, we prove that the stochastic model
can be transformed into a normal form near the folded node, which can be linked
to recent results on the interplay between deterministic and stochastic small
amplitude oscillations. The normal form can also be used to study the parameter
influence on the noise level near folded singularities.
