Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysis
In this article, we reconsider the classical target cell limited dynamical within-host HIV model, solely taking into account the interaction between $ {\rm{CD}}4^{+} $ T cells and virus particles. First, we summarize some analytical results regarding the corresponding dynamical system. For that pur...
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AIMS Press
2024-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2024343 |
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| author | Benjamin Wacker |
| author_facet | Benjamin Wacker |
| author_sort | Benjamin Wacker |
| collection | DOAJ |
| description | In this article, we reconsider the classical target cell limited dynamical within-host HIV model, solely taking into account the interaction between $ {\rm{CD}}4^{+} $ T cells and virus particles. First, we summarize some analytical results regarding the corresponding dynamical system. For that purpose, we proved some analytical results regarding the system of differential equations as our first main contribution. Specifically, we showed non-negativity and boundedness of solutions, global existence in time and global uniqueness in time and examined stability properties of two possible equilibria. In particular, we demonstrated that the virus-free equilibrium and the plateau-phase equilibrium are locally asymptotically stable using the Routh–Hurwitz criterion under appropriate conditions. As our second main contribution, we underline our theoretical findings through some numerical experiments with standard Runge–Kutta time stepping schemes. We conclude this work with a summary of our main results and a suggestion of an extension for more complex dynamical systems with regard to HIV-infection. |
| format | Article |
| id | doaj-art-5dedaae9518b43c68382daabb64c1b3a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5dedaae9518b43c68382daabb64c1b3a2025-01-23T05:05:30ZengAIMS PressMathematical Biosciences and Engineering1551-00182024-12-0121127805782910.3934/mbe.2024343Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysisBenjamin Wacker0Department of Engineering and Natural Sciences, University of Applied Sciences Merseburg, Eberhard-Leibnitz-Str. 2, D-06217 Merseburg, GermanyIn this article, we reconsider the classical target cell limited dynamical within-host HIV model, solely taking into account the interaction between $ {\rm{CD}}4^{+} $ T cells and virus particles. First, we summarize some analytical results regarding the corresponding dynamical system. For that purpose, we proved some analytical results regarding the system of differential equations as our first main contribution. Specifically, we showed non-negativity and boundedness of solutions, global existence in time and global uniqueness in time and examined stability properties of two possible equilibria. In particular, we demonstrated that the virus-free equilibrium and the plateau-phase equilibrium are locally asymptotically stable using the Routh–Hurwitz criterion under appropriate conditions. As our second main contribution, we underline our theoretical findings through some numerical experiments with standard Runge–Kutta time stepping schemes. We conclude this work with a summary of our main results and a suggestion of an extension for more complex dynamical systems with regard to HIV-infection.https://www.aimspress.com/article/doi/10.3934/mbe.2024343dynamical systemequilibriaexistencenon-negativitystabilityuniquenesswithin-host hiv model |
| spellingShingle | Benjamin Wacker Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysis Mathematical Biosciences and Engineering dynamical system equilibria existence non-negativity stability uniqueness within-host hiv model |
| title | Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysis |
| title_full | Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysis |
| title_fullStr | Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysis |
| title_full_unstemmed | Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysis |
| title_short | Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysis |
| title_sort | revisiting the classical target cell limited dynamical within host hiv model basic mathematical properties and stability analysis |
| topic | dynamical system equilibria existence non-negativity stability uniqueness within-host hiv model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2024343 |
| work_keys_str_mv | AT benjaminwacker revisitingtheclassicaltargetcelllimiteddynamicalwithinhosthivmodelbasicmathematicalpropertiesandstabilityanalysis |