Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 434, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.physd.2022.133268
Keywords
SIR model; Seasonality; Basic reproduction number; Backward bifurcation; Strange attractors; Observable chaos
Categories
Funding
- FEDER via COMPETE 2020 -POCI [MAGIC POCI-01-0145-FEDER-032485]
- FCT/MCTES via PIDDAC
- CMUP, Portugal - Fundacao para a Ciencia e a Tecnologia (FCT) [UIBD/MAT/00144/2020]
- European structural funds through the programs FEDER, under the partnership agreement PT2020
- FCT [CEECIND/01075/2020]
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This study analyzed a multiparameter periodically-forced dynamical system inspired by the SIR endemic model, and found that R-0 < 1 is not sufficient to eliminate infectious individuals. The study also proposed a new attractor theory approach.
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.
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