  The interplay of seasonality, the system's nonlinearities and intrinsic
stochasticity is studied for a seasonally forced
susceptible-exposed-infective-recovered stochastic model. The model is explored
in the parameter region that corresponds to childhood infectious diseases such
as measles. The power spectrum of the stochastic fluctuations around the
attractors of the deterministic system that describes the model in the
thermodynamic limit is computed analytically and validated by stochastic
simulations for large system sizes. Size effects are studied through additional
simulations. Other effects such as switching between coexisting attractors
induced by stochasticity often mentioned in the literature as playing an
important role in the dynamics of childhood infectious diseases are also
investigated. The main conclusion is that stochastic amplification, rather than
these effects, is the key ingredient to understand the observed incidence
patterns.
