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J Theor Biol. 1984 Oct 21;110(4):665-79.

Seasonality and period-doubling bifurcations in an epidemic model.


The annual incidence rates of some endemic infectious diseases are steady while others fluctuate dramatically, often in a regular cycle. In order to investigate the role of seasonality in driving cycles of recurrent epidemics, we analyze numerically the susceptible/exposed/infective/recovered (SEIR) epidemic model with seasonal transmission. We show that small amplitude periodic solutions exhibit a sequence of period-doubling bifurcations as the amplitude of seasonal variation increases, predicting a transition to chaos of the kind studied in other biological contexts. The epidemiological implication is that the seasonal mechanism generating biennial epidemics may not be able to account for small-amplitude recurrent epidemics of arbitrary periodicity.

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