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Strange attractors in the seasonally forced epidemic SIR model

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 نشر من قبل Jo\\~ao Maur\\'icio de Carvalho
 تاريخ النشر 2021
  مجال البحث
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We analyse a periodically-forced SIR model to investigate the influence of seasonality on the disease dynamics and we show that the condition on the basic reproduction number $mathcal{R}_0<1$ is not enough to guarantee the elimination of the disease. Using the theory of rank-one attractors, for an open subset in the space of parameters of the model for which $mathcal{R}_0<1$, the flow exhibits persistent strange attractors, producing infinitely many periodic and aperiodic patterns. Although numerical experiments have already suggested that periodically-forced SIR model may exhibit observable chaos, a rigorous proof was not given before. Our results agree well with the empirical belief that intense seasonality induces chaos. This should serve as a warning to all doing numerics (on epidemiological models) who deduce that the disease disappears merely because $mathcal{R}_0<1$.



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