Deterministic models for recurrent epidemics are studied via a comparison with the corresponding fully stochastic models. Deterministic models with periodic contact rate, where chaos occurs, require extremely and unreasonably large population sizes to be acceptable. The mechanism that drives chaos in these models is caused by an unacceptable mathematical approximation. The chaotic behaviour is upset by minute amounts of external infection. We conclude that recognition of demographic stochasticity is necessary in the study of recurrent epidemics.

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1998-1999 Mathematics in Biology