Stability of HIV-1 Dynamics Models with Viral and Cellular Infections in the Presence of Macrophages
In this research work, we suggest two mathematical models that take into account (i) two categories of target cells, CD<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>4</mn><mo>+</...
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MDPI AG
2023-06-01
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| Online Access: | https://www.mdpi.com/2075-1680/12/7/617 |
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| author | Aeshah A. Raezah Elsayed Dahy E. Kh. Elnahary Shaimaa A. Azoz |
| author_facet | Aeshah A. Raezah Elsayed Dahy E. Kh. Elnahary Shaimaa A. Azoz |
| author_sort | Aeshah A. Raezah |
| collection | DOAJ |
| description | In this research work, we suggest two mathematical models that take into account (i) two categories of target cells, CD<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>4</mn><mo>+</mo></msup></semantics></math></inline-formula>T cells and macrophages, and (ii) two modes of infection transmissions, the direct virus-to-cell (VTC) method and cell-to-cell (CTC) infection transmission, where CTC is an effective method of spreading human immunodeficiency virus type-1 (HIV-1), as with the VTC method. The second model incorporates four time delays. In both models, the presence of a bounded and positive solution of the biological model is investigated. The existence conditions of all equilibria are established. The basic reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mn>0</mn></msub></semantics></math></inline-formula> that identifies a disease index is obtained. Lyapunov functions are utilized to verify the global stability of all equilibria. The theoretical findings are verified through numerical simulations. According to the outcomes, the trajectories of the solutions approach the infection-free equilibrium and infection-present equilibrium when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, respectively. Further, we study the sensitivity analysis to investigate how the values of all the parameters of the suggested model affect <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mn>0</mn></msub></semantics></math></inline-formula> for given data. We discuss the impact of the time delay on HIV-1 progression. We find that a longer time delay results in suppression of the HIV-1 infection and vice versa. |
| first_indexed | 2024-03-11T01:19:02Z |
| format | Article |
| id | doaj.art-e483d4ea00e14e70b4917addad3d0e79 |
| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-03-11T01:19:02Z |
| publishDate | 2023-06-01 |
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| spelling | doaj.art-e483d4ea00e14e70b4917addad3d0e792023-11-18T18:17:03ZengMDPI AGAxioms2075-16802023-06-0112761710.3390/axioms12070617Stability of HIV-1 Dynamics Models with Viral and Cellular Infections in the Presence of MacrophagesAeshah A. Raezah0Elsayed Dahy1E. Kh. Elnahary2Shaimaa A. Azoz3Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut 71524, EgyptDepartment of Mathematics, Faculty of Science, Sohag University, Sohag 82524, EgyptDepartment of Mathematics, Faculty of Science, Assiut University, Assiut 71516, EgyptIn this research work, we suggest two mathematical models that take into account (i) two categories of target cells, CD<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>4</mn><mo>+</mo></msup></semantics></math></inline-formula>T cells and macrophages, and (ii) two modes of infection transmissions, the direct virus-to-cell (VTC) method and cell-to-cell (CTC) infection transmission, where CTC is an effective method of spreading human immunodeficiency virus type-1 (HIV-1), as with the VTC method. The second model incorporates four time delays. In both models, the presence of a bounded and positive solution of the biological model is investigated. The existence conditions of all equilibria are established. The basic reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mn>0</mn></msub></semantics></math></inline-formula> that identifies a disease index is obtained. Lyapunov functions are utilized to verify the global stability of all equilibria. The theoretical findings are verified through numerical simulations. According to the outcomes, the trajectories of the solutions approach the infection-free equilibrium and infection-present equilibrium when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, respectively. Further, we study the sensitivity analysis to investigate how the values of all the parameters of the suggested model affect <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mn>0</mn></msub></semantics></math></inline-formula> for given data. We discuss the impact of the time delay on HIV-1 progression. We find that a longer time delay results in suppression of the HIV-1 infection and vice versa.https://www.mdpi.com/2075-1680/12/7/617HIV-1 infectionLyapunov functionglobal stabilitytime delaysensitivity analysis |
| spellingShingle | Aeshah A. Raezah Elsayed Dahy E. Kh. Elnahary Shaimaa A. Azoz Stability of HIV-1 Dynamics Models with Viral and Cellular Infections in the Presence of Macrophages Axioms HIV-1 infection Lyapunov function global stability time delay sensitivity analysis |
| title | Stability of HIV-1 Dynamics Models with Viral and Cellular Infections in the Presence of Macrophages |
| title_full | Stability of HIV-1 Dynamics Models with Viral and Cellular Infections in the Presence of Macrophages |
| title_fullStr | Stability of HIV-1 Dynamics Models with Viral and Cellular Infections in the Presence of Macrophages |
| title_full_unstemmed | Stability of HIV-1 Dynamics Models with Viral and Cellular Infections in the Presence of Macrophages |
| title_short | Stability of HIV-1 Dynamics Models with Viral and Cellular Infections in the Presence of Macrophages |
| title_sort | stability of hiv 1 dynamics models with viral and cellular infections in the presence of macrophages |
| topic | HIV-1 infection Lyapunov function global stability time delay sensitivity analysis |
| url | https://www.mdpi.com/2075-1680/12/7/617 |
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