Open AccessA singularly perturbed SIS model with age structure
Author(s) -
Jacek Banasiak,
Eddy Kimba Phongi,
Mirosław Lachowicz
Publication year - 2013
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2013.10.499
Subject(s) - tikhonov regularization , mathematics , nonlinear system , focus (optics) , epidemic model , age structure , calculus (dental) , econometrics , mathematical analysis , inverse problem , demography , medicine , physics , dentistry , quantum mechanics , optics , population , sociology
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.