| Abstract | Seasonality is a complex force in nature, and may affect multiple processes in a population. Seasonal variations may, therefore, have a considerable effect on the transmission dynamics of a pathogen. In this talk, a seasonally perturbed Susceptible-Infected-Recovered (SIR) model is considered. Such a system is known to exhibit complex dynamics as the amplitude of the seasonal perturbation term is increased. Furthermore, it has been long observed that chaotic solutions may appear in such a model. The results of computer simulations of this seasonally perturbed SIR system suggest evidence of the existence of chaos in the model. A rigorous proof of the existence of chaos in this system will be outlined. The proof is based on the concept of topological hyperbolicity, which will be discussed informally in this talk. To our knowledge, this is the first time that this technique has been used to prove the existence of chaos in an epidemiological model. |
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