  Rubella is a completely immunizing and mild infection in children.
Understanding its behavior is of considerable public health importance because
of Congenital Rubella Syndrome, which results from infection with rubella
during early pregnancy and may entail a variety of birth defects. The recurrent
dynamics of rubella are relatively poorly resolved, and appear to show
considerable diversity globally. Here, we investigate the behavior of a
stochastic seasonally forced susceptible-infected-recovered model to
characterize the determinants of these dynamics and illustrate patterns by
comparison with measles. We perform a systematic analysis of spectra of
stochastic fluctuations around stable attractors of the corresponding
deterministic model and compare them with spectra from full stochastic
simulations in large populations. This approach allows us to quantify the
effects of demographic stochasticity and to give a coherent picture of measles
and rubella dynamics, explaining essential differences in the recurrent
patterns exhibited by these diseases. We discuss the implications of our
findings in the context of vaccination and changing birth rates as well as the
persistence of these two childhood infections.
