Strange attractors in a seasonally forced epidemic SIR model

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.

Date and Venue

Start Date
Venue
FC1.031

Speaker

João Carvalho

Speaker's Institution

PhD Student- CMUP

Area

Dynamical Systems