Canard-type solutions in epidemiological models

Jacek Banasiak; Eddy Kimba Phongi

doi:10.3934/proc.2015.0085

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2015, Volume 2015: 85-93. Doi: 10.3934/proc.2015.0085 open access

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Canard-type solutions in epidemiological models

Jacek Banasiak^1, and
Eddy Kimba Phongi^2,

1.
School of Mathematical Sciences, UKZN, Durban
2.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041

Received: August 31, 2014

Revised: December 31, 2014

Published: October 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 34E15, 92A15; Secondary: 34E13.

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References

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