Ganna Rozhnova, C. Jessica E. Metcalf, Bryan T. Grenfell
The 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 stochasticity and to give a coherent picture of measles and rubella dynamics, explaining essential differences in the 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.
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http://arxiv.org/abs/1212.4390
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