Mathematical Biosciences and Engineering, 2013, 10(3): 499-521. doi: 10.3934/mbe.2013.10.499.

Primary: 34E15, 92D30; Secondary: 34E13.

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A singularly perturbed SIS model with age structure

1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban
2. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041
3. Institute of Applied Mathematics and Mechanics, University of Warsaw, Warsaw

We present a preliminary study of an SIS model with a basic age structure and we focus on a disease with quick turnover, such as influenza or common cold. In such a case the difference between the characteristic demographic and epidemiological times naturally introduces two time scales in the model which makes it singularly perturbed. Using the Tikhonov theorem we prove that for certain classes of initial conditions the nonlinear structured SIS model can be approximated with very good accuracy by lower dimensional linear models.
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Keywords singularly perturbed dynamical systems; population dynamics; SIS system; Tikhonov theorem.; age structure; multiple time scales

Citation: Jacek Banasiak, Eddy Kimba Phongi, MirosŁaw Lachowicz. A singularly perturbed SIS model with age structure. Mathematical Biosciences and Engineering, 2013, 10(3): 499-521. doi: 10.3934/mbe.2013.10.499

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