title: Seasonality and period-doubling bifurcations in an epidemic model.
abstract: 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.
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology*; D004196:Disease Outbreaks / Q000453:epidemiology*; D004739:England; D006801:Humans; D008433:Mathematics; D008457:Measles / Q000453:epidemiology; D008954:Models, Biological; D009519:New York City; D010507:Periodicity; D012621:Seasons; D013997:Time Factors; D014852:Wales