A singularly perturbed HIV model with treatment and antigenic variation
We study the long term dynamics and the multiscale aspects of a within-host HIV model that takes into account both mutation and treatment with enzyme inhibitors. This model generalizes a number of other models that have been extensively used to describe the HIV dynamics. Since the free virus dyna...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1 |
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| _version_ | 1832590097162174464 |
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| author | Nara Bobko Jorge P. Zubelli |
| author_facet | Nara Bobko Jorge P. Zubelli |
| author_sort | Nara Bobko |
| collection | DOAJ |
| description | We study the long term dynamics and the multiscale aspects of a within-host HIV model that takes into account both mutation and treatment with enzyme inhibitors. This model generalizes a number of other models that have been extensively used to describe the HIV dynamics. Since the free virus dynamics occur on a much faster time-scale than cell dynamics, the model has two intrinsic time scales and should be viewed as a singularly perturbed system. Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. Furthermore, we show that this reduced system is globally asymptotically stable by using Lyapunov's stability theory. |
| format | Article |
| id | doaj-art-0caebf080fba4080910a53975b78f09a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-0caebf080fba4080910a53975b78f09a2025-01-24T02:31:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-0112112110.3934/mbe.2015.12.1A singularly perturbed HIV model with treatment and antigenic variationNara Bobko0Jorge P. Zubelli1Instituto Nacional de Matemática Pura e Aplicada, Rio do Janeiro, RJ 22460-320Instituto Nacional de Matemática Pura e Aplicada, Rio do Janeiro, RJ 22460-320We study the long term dynamics and the multiscale aspects of a within-host HIV model that takes into account both mutation and treatment with enzyme inhibitors. This model generalizes a number of other models that have been extensively used to describe the HIV dynamics. Since the free virus dynamics occur on a much faster time-scale than cell dynamics, the model has two intrinsic time scales and should be viewed as a singularly perturbed system. Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. Furthermore, we show that this reduced system is globally asymptotically stable by using Lyapunov's stability theory.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1immune responselyapunov functions.global stabilitymultiscale analysishivmutation |
| spellingShingle | Nara Bobko Jorge P. Zubelli A singularly perturbed HIV model with treatment and antigenic variation Mathematical Biosciences and Engineering immune response lyapunov functions. global stability multiscale analysis hiv mutation |
| title | A singularly perturbed HIV model with treatment and antigenic variation |
| title_full | A singularly perturbed HIV model with treatment and antigenic variation |
| title_fullStr | A singularly perturbed HIV model with treatment and antigenic variation |
| title_full_unstemmed | A singularly perturbed HIV model with treatment and antigenic variation |
| title_short | A singularly perturbed HIV model with treatment and antigenic variation |
| title_sort | singularly perturbed hiv model with treatment and antigenic variation |
| topic | immune response lyapunov functions. global stability multiscale analysis hiv mutation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1 |
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