title: A singularly perturbed SIS model with age structure.
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.
authors.affiliation: School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa. banasiak@ukzn.ac.za
authors.forename: Jacek
authors.initials: J
authors.lastname: Banasiak
authors.forename: Eddy Kimba
authors.initials: EK
authors.lastname: Phongi
authors.forename: Mirosław
authors.initials: M
authors.lastname: Lachowicz
mesh_terms: D000367:Age Factors; D016021:Epidemiologic Studies; D006801:Humans; D055641:Mathematical Concepts; D015233:Models, Statistical; D011157:Population Dynamics; D049490:Systems Biology