Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models

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Abstract
A seasonally forced nonlinear SEIR epidemic model is used to simulate small and large amplitude periodic outbreaks. The model is shown to exhibit bistable behavior for a fixed set of parameters. Basins of attraction for each recurrent outbreak are computed, and it is shown that the basins of two coexisting stable outbreaks are intertwined in a complicated manner. The effect of such a basin structure is shown to result in an obstruction in predicting asymptotically the type of outbreak given an uncertainty in the initial population of susceptibles and infectives.

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