A singularly perturbed SIS model with age structure

Jacek Banasiak; Eddy Kimba Phongi; MirosŁaw Lachowicz

doi:10.3934/mbe.2013.10.499

Article Contents

2013, Volume 10, Issue 3: 499-521. Doi: 10.3934/mbe.2013.10.499

This issue Previous Article From the guest editors Next Article Diffusion rate determines balance between extinction and proliferation in birth-death processes

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

Received: April 30, 2012

Revised: July 31, 2012

Published: March 2013

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Abstract

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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Mathematics Subject Classification: Primary: 34E15, 92D30; Secondary: 34E13.

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References

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