Mathematical analysis of a HIV model with frequency dependence and viral diversity
We consider the effect of viral diversity on the human immune sys-tem with the frequency dependent proliferation rate of CTLs and the elimina-tion rate of infected cells by CTLs. The model has very complex mathematicalstructures such as limit cycle, quasi-periodic attractors, chaotic attractors, and...
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| Format: | Article |
| Language: | English |
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AIMS Press
2008-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.457 |
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| _version_ | 1832590165379383296 |
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| author | Shingo Iwami Shinji Nakaoka Yasuhiro Takeuchi |
| author_facet | Shingo Iwami Shinji Nakaoka Yasuhiro Takeuchi |
| author_sort | Shingo Iwami |
| collection | DOAJ |
| description | We consider the effect of viral diversity on the human immune sys-tem with the frequency dependent proliferation rate of CTLs and the elimina-tion rate of infected cells by CTLs. The model has very complex mathematicalstructures such as limit cycle, quasi-periodic attractors, chaotic attractors, andso on. To understand the complexity we investigate the global behavior of themodel and demonstrate the existence and stability conditions of the equilibria.Further we give some theoretical considerations obtained by our mathematicalmodel to HIV infection. |
| format | Article |
| id | doaj-art-0e44e525ccad4227a39890b7507592b2 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2008-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-0e44e525ccad4227a39890b7507592b22025-01-24T01:58:23ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-05-015345747610.3934/mbe.2008.5.457Mathematical analysis of a HIV model with frequency dependence and viral diversityShingo Iwami0Shinji Nakaoka1Yasuhiro Takeuchi2Graduate School of Science and Technology, Shizuoka University, 3-5-1 Johoku Naka-ku Hamamatsu 432-8561Graduate School of Science and Technology, Shizuoka University, 3-5-1 Johoku Naka-ku Hamamatsu 432-8561Graduate School of Science and Technology, Shizuoka University, 3-5-1 Johoku Naka-ku Hamamatsu 432-8561We consider the effect of viral diversity on the human immune sys-tem with the frequency dependent proliferation rate of CTLs and the elimina-tion rate of infected cells by CTLs. The model has very complex mathematicalstructures such as limit cycle, quasi-periodic attractors, chaotic attractors, andso on. To understand the complexity we investigate the global behavior of themodel and demonstrate the existence and stability conditions of the equilibria.Further we give some theoretical considerations obtained by our mathematicalmodel to HIV infection.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.457frequencydependenceviral diversitystability analysis.hiv model |
| spellingShingle | Shingo Iwami Shinji Nakaoka Yasuhiro Takeuchi Mathematical analysis of a HIV model with frequency dependence and viral diversity Mathematical Biosciences and Engineering frequencydependence viral diversity stability analysis. hiv model |
| title | Mathematical analysis of a HIV model with frequency dependence and viral diversity |
| title_full | Mathematical analysis of a HIV model with frequency dependence and viral diversity |
| title_fullStr | Mathematical analysis of a HIV model with frequency dependence and viral diversity |
| title_full_unstemmed | Mathematical analysis of a HIV model with frequency dependence and viral diversity |
| title_short | Mathematical analysis of a HIV model with frequency dependence and viral diversity |
| title_sort | mathematical analysis of a hiv model with frequency dependence and viral diversity |
| topic | frequencydependence viral diversity stability analysis. hiv model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.457 |
| work_keys_str_mv | AT shingoiwami mathematicalanalysisofahivmodelwithfrequencydependenceandviraldiversity AT shinjinakaoka mathematicalanalysisofahivmodelwithfrequencydependenceandviraldiversity AT yasuhirotakeuchi mathematicalanalysisofahivmodelwithfrequencydependenceandviraldiversity |