Global stability of a class of discreteage-structured SIS models with immigration
Immigration has an important influence on the growth of populationand the transmission dynamics of infectious diseases. A discreteage-structured epidemic SIS model with immigration is formulated andits dynamical behavior is studied in this paper. It is found thatpopulation growth will be determined...
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| Format: | Article |
| Language: | English |
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AIMS Press
2009-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.409 |
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| _version_ | 1832590165157085184 |
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| author | Yicang Zhou Zhien Ma |
| author_facet | Yicang Zhou Zhien Ma |
| author_sort | Yicang Zhou |
| collection | DOAJ |
| description | Immigration has an important influence on the growth of populationand the transmission dynamics of infectious diseases. A discreteage-structured epidemic SIS model with immigration is formulated andits dynamical behavior is studied in this paper. It is found thatpopulation growth will be determined by the reproductive numberand the immigration rate. In the simple case without infectedimmigration, the basic reproductive number is defined, and theglobal stability of equilibria is investigated. In the case withinfected immigration, there is no disease-free equilibrium, andthere always exists an endemic equilibrium, and the global stabilityconditions of the unique endemic equilibrium is obtained. |
| format | Article |
| id | doaj-art-0d50eb98d1c04467990e2766a3c10e0e |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-0d50eb98d1c04467990e2766a3c10e0e2025-01-24T01:59:06ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-02-016240942510.3934/mbe.2009.6.409Global stability of a class of discreteage-structured SIS models with immigrationYicang Zhou0Zhien Ma1Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049Immigration has an important influence on the growth of populationand the transmission dynamics of infectious diseases. A discreteage-structured epidemic SIS model with immigration is formulated andits dynamical behavior is studied in this paper. It is found thatpopulation growth will be determined by the reproductive numberand the immigration rate. In the simple case without infectedimmigration, the basic reproductive number is defined, and theglobal stability of equilibria is investigated. In the case withinfected immigration, there is no disease-free equilibrium, andthere always exists an endemic equilibrium, and the global stabilityconditions of the unique endemic equilibrium is obtained.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.409age-structureinfectious diseasediscrete modelstability. |
| spellingShingle | Yicang Zhou Zhien Ma Global stability of a class of discreteage-structured SIS models with immigration Mathematical Biosciences and Engineering age-structure infectious disease discrete model stability. |
| title | Global stability of a class of discreteage-structured SIS models with immigration |
| title_full | Global stability of a class of discreteage-structured SIS models with immigration |
| title_fullStr | Global stability of a class of discreteage-structured SIS models with immigration |
| title_full_unstemmed | Global stability of a class of discreteage-structured SIS models with immigration |
| title_short | Global stability of a class of discreteage-structured SIS models with immigration |
| title_sort | global stability of a class of discreteage structured sis models with immigration |
| topic | age-structure infectious disease discrete model stability. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.409 |
| work_keys_str_mv | AT yicangzhou globalstabilityofaclassofdiscreteagestructuredsismodelswithimmigration AT zhienma globalstabilityofaclassofdiscreteagestructuredsismodelswithimmigration |