We analyse the forced SIR model to investigate the influence of seasonality on the disease dynamics. Seasonality is often introduced in epidemic models via a transmission rate of sinusoidal type. In this talk, we present two results related to this model:
(i) the condition on the basic reproduction number R0 < 1 is not enough to guarantee the elimination of the disease;
(ii) for R0 < 1, using the theory of Rank-one attractors developed by Wang and Young, the flow exhibits persistent strange attractors.
Although numerical experiments have already suggested that periodically-forced SIR model may exhibit chaos, a rigorous proof (without computer-aided) was not given before. Our results are consistent with the empirical belief that intense seasonality induces chaos.