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Canard-type solutions in epidemiological models

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  • The paper concerns an epidemiological model with an age structure and with two time scales: the slow one refers to the demographical processes and the fast describes the dynamics of a fast disease such as flu or common cold. The model in the singular limit corresponding to the infinite disease-related rates has two intersecting quasi-stationary steady states. We investigate the asymptotic behaviour of solutions passing close to the intersection manifold and show that in the models with increasing total populations there is a delay in switching between the quasi-stationary states which resembles the so-called canard solutions.
    Mathematics Subject Classification: Primary: 34E15, 92A15; Secondary: 34E13.


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