A singularly perturbed SIS model with age structure
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 mod...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.499 |
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| author | Jacek Banasiak Eddy Kimba Phongi MirosŁaw Lachowicz |
| author_facet | Jacek Banasiak Eddy Kimba Phongi MirosŁaw Lachowicz |
| author_sort | Jacek Banasiak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-381afd79ef794216acb25f2268e14878 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-381afd79ef794216acb25f2268e148782025-01-24T02:26:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-03-0110349952110.3934/mbe.2013.10.499A singularly perturbed SIS model with age structureJacek Banasiak0Eddy Kimba Phongi1MirosŁaw Lachowicz2School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, DurbanSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, DurbanSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, DurbanWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.499singularly perturbed dynamical systemspopulation dynamicssis systemtikhonov theorem.age structuremultiple time scales |
| spellingShingle | Jacek Banasiak Eddy Kimba Phongi MirosŁaw Lachowicz A singularly perturbed SIS model with age structure Mathematical Biosciences and Engineering singularly perturbed dynamical systems population dynamics sis system tikhonov theorem. age structure multiple time scales |
| title | A singularly perturbed SIS model with age structure |
| title_full | A singularly perturbed SIS model with age structure |
| title_fullStr | A singularly perturbed SIS model with age structure |
| title_full_unstemmed | A singularly perturbed SIS model with age structure |
| title_short | A singularly perturbed SIS model with age structure |
| title_sort | singularly perturbed sis model with age structure |
| topic | singularly perturbed dynamical systems population dynamics sis system tikhonov theorem. age structure multiple time scales |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.499 |
| work_keys_str_mv | AT jacekbanasiak asingularlyperturbedsismodelwithagestructure AT eddykimbaphongi asingularlyperturbedsismodelwithagestructure AT mirosławlachowicz asingularlyperturbedsismodelwithagestructure AT jacekbanasiak singularlyperturbedsismodelwithagestructure AT eddykimbaphongi singularlyperturbedsismodelwithagestructure AT mirosławlachowicz singularlyperturbedsismodelwithagestructure |