Dynamics of HIV-1/HTLV-I Co-Infection Model with Humoral Immunity and Cellular Infection
Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses which infect the same target, CD<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>4&l...
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MDPI AG
2022-08-01
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| Series: | Viruses |
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| Online Access: | https://www.mdpi.com/1999-4915/14/8/1719 |
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| author | Noura H. AlShamrani Matuka A. Alshaikh Ahmed M. Elaiw Khalid Hattaf |
| author_facet | Noura H. AlShamrani Matuka A. Alshaikh Ahmed M. Elaiw Khalid Hattaf |
| author_sort | Noura H. AlShamrani |
| collection | DOAJ |
| description | Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses which infect the same target, 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. This type of cell is considered the main component of the immune system. Since both viruses have the same means of transmission between individuals, HIV-1-infected patients are more exposed to the chance of co-infection with HTLV-I, and vice versa, compared to the general population. The mathematical modeling and analysis of within-host HIV-1/HTLV-I co-infection dynamics can be considered a robust tool to support biological and medical research. In this study, we have formulated and analyzed an HIV-1/HTLV-I co-infection model with humoral immunity, taking into account both latent HIV-1-infected cells and HTLV-I-infected cells. The model considers two modes of HIV-1 dissemination, virus-to-cell (V-T-C) and cell-to-cell (C-T-C). We prove the nonnegativity and boundedness of the solutions of the model. We find all steady states of the model and establish their existence conditions. We utilize Lyapunov functions and LaSalle’s invariance principle to investigate the global stability of all the steady states of the model. Numerical simulations were performed to illustrate the corresponding theoretical results. The effects of humoral immunity and C-T-C transmission on the HIV-1/HTLV-I co-infection dynamics are discussed. We have shown that humoral immunity does not play the role of clearing an HIV-1 infection but it can control HIV-1 infection. Furthermore, we note that the omission of C-T-C transmission from the HIV-1/HTLV-I co-infection model leads to an under-evaluation of the basic HIV-1 mono-infection reproductive ratio. |
| first_indexed | 2024-03-09T03:42:44Z |
| format | Article |
| id | doaj.art-b30915d2d74f4d3bacfea64126535e30 |
| institution | Directory Open Access Journal |
| issn | 1999-4915 |
| language | English |
| last_indexed | 2024-03-09T03:42:44Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Viruses |
| spelling | doaj.art-b30915d2d74f4d3bacfea64126535e302023-12-03T14:39:14ZengMDPI AGViruses1999-49152022-08-01148171910.3390/v14081719Dynamics of HIV-1/HTLV-I Co-Infection Model with Humoral Immunity and Cellular InfectionNoura H. AlShamrani0Matuka A. Alshaikh1Ahmed M. Elaiw2Khalid Hattaf3Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21974, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaEquipe de Recherche en Modélisation et Enseignement des Mathématiques (ERMEM), Centre Régional des Métiers de l’Education et de la Formation (CRMEF), Derb Ghalef, Casablanca 20340, MoroccoHuman immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses which infect the same target, 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. This type of cell is considered the main component of the immune system. Since both viruses have the same means of transmission between individuals, HIV-1-infected patients are more exposed to the chance of co-infection with HTLV-I, and vice versa, compared to the general population. The mathematical modeling and analysis of within-host HIV-1/HTLV-I co-infection dynamics can be considered a robust tool to support biological and medical research. In this study, we have formulated and analyzed an HIV-1/HTLV-I co-infection model with humoral immunity, taking into account both latent HIV-1-infected cells and HTLV-I-infected cells. The model considers two modes of HIV-1 dissemination, virus-to-cell (V-T-C) and cell-to-cell (C-T-C). We prove the nonnegativity and boundedness of the solutions of the model. We find all steady states of the model and establish their existence conditions. We utilize Lyapunov functions and LaSalle’s invariance principle to investigate the global stability of all the steady states of the model. Numerical simulations were performed to illustrate the corresponding theoretical results. The effects of humoral immunity and C-T-C transmission on the HIV-1/HTLV-I co-infection dynamics are discussed. We have shown that humoral immunity does not play the role of clearing an HIV-1 infection but it can control HIV-1 infection. Furthermore, we note that the omission of C-T-C transmission from the HIV-1/HTLV-I co-infection model leads to an under-evaluation of the basic HIV-1 mono-infection reproductive ratio.https://www.mdpi.com/1999-4915/14/8/1719HIV-1/HTLV-I co-infectionhumoral immunitycell-to-cell infectionglobal stabilityLyapunov function |
| spellingShingle | Noura H. AlShamrani Matuka A. Alshaikh Ahmed M. Elaiw Khalid Hattaf Dynamics of HIV-1/HTLV-I Co-Infection Model with Humoral Immunity and Cellular Infection Viruses HIV-1/HTLV-I co-infection humoral immunity cell-to-cell infection global stability Lyapunov function |
| title | Dynamics of HIV-1/HTLV-I Co-Infection Model with Humoral Immunity and Cellular Infection |
| title_full | Dynamics of HIV-1/HTLV-I Co-Infection Model with Humoral Immunity and Cellular Infection |
| title_fullStr | Dynamics of HIV-1/HTLV-I Co-Infection Model with Humoral Immunity and Cellular Infection |
| title_full_unstemmed | Dynamics of HIV-1/HTLV-I Co-Infection Model with Humoral Immunity and Cellular Infection |
| title_short | Dynamics of HIV-1/HTLV-I Co-Infection Model with Humoral Immunity and Cellular Infection |
| title_sort | dynamics of hiv 1 htlv i co infection model with humoral immunity and cellular infection |
| topic | HIV-1/HTLV-I co-infection humoral immunity cell-to-cell infection global stability Lyapunov function |
| url | https://www.mdpi.com/1999-4915/14/8/1719 |
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