Strange attractors in a dynamical system inspired by a seasonally forced SIR model

We analyze a multiparameter periodically-forced dynamical system inspired in the SIR endemic model. We show that the condition on the basic reproduction number R-0 < 1 is not sufficient to guarantee the elimination of Infectious individuals due to a backward bifurcation. Using the theory of rank-one attractors, for an open subset in the space of parameters where R-0 < 1, the flow exhibits persistent strange attractors. These sets are not confined to a tubular neighborhood in the phase space, shadow the ghost of a two-dimensional invariant torus and are numerically observable. Although numerical experiments have already suggested that periodically-forced biological models 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 work provides a preliminary investigation of the interplay between seasonality, deterministic dynamics and the prevalence of strange attractors in a nonlinear forced system inspired by biology. (c) 2022 Elsevier B.V. All rights reserved.