Backward bifurcation on HIV/AIDS SEI1I2TAR model with multiple interactions between sub-populations
AbstractThe HIV/AIDS model was dynamically analyzed in this study. The model has seven compartments: the uneducated, the educated, the HIV-positive who take antiretroviral therapy (ART), the HIV-positive who do not take ART, people receiving ART treatment, people with AIDS who do not receive any tre...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | Arab Journal of Basic and Applied Sciences |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/25765299.2023.2286713 |
| _version_ | 1797394368857899008 |
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| author | Ummu Habibah Trisilowati Tiara Rizki Tania Labib Umam Al-Faruq |
| author_facet | Ummu Habibah Trisilowati Tiara Rizki Tania Labib Umam Al-Faruq |
| author_sort | Ummu Habibah |
| collection | DOAJ |
| description | AbstractThe HIV/AIDS model was dynamically analyzed in this study. The model has seven compartments: the uneducated, the educated, the HIV-positive who take antiretroviral therapy (ART), the HIV-positive who do not take ART, people receiving ART treatment, people with AIDS who do not receive any treatment (full-blown AIDS), and the recovered. This model takes into account the analysis of the multiple interactions between the uneducated and the educated subpopulations, the HIV-positive who take and who do not take ART. The free-disease and endemic equilibrium points, as well as the basic reproduction number [Formula: see text] as a limit condition for infection-free and endemic occurrence, were produced by a mathematical analysis. The center-manifold hypothesis was used to prove that a backward bifurcation exists. The free-disease and endemic equilibrium points coexist when [Formula: see text] This means that HIV/AIDS is still spreading. A basic reproduction number below one is insufficient to constitute a free-disease condition. In order to determine essential parameters that significantly contribute to HIV/AIDS transmission, we computed sensitivity index values using a sensitivity analysis. The HIV/AIDS model and bifurcation parameter both identified the rate of HIV transmission from uneducated individuals to HIV-positive individuals who do not receive ART as the most crucial parameter. A numerical simulation supports the dynamical analysis. |
| first_indexed | 2024-03-09T00:18:44Z |
| format | Article |
| id | doaj.art-cacf4303dc2a438a9acacd55fbad3c57 |
| institution | Directory Open Access Journal |
| issn | 2576-5299 |
| language | English |
| last_indexed | 2024-03-09T00:18:44Z |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj.art-cacf4303dc2a438a9acacd55fbad3c572023-12-12T06:40:42ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992024-12-01311183110.1080/25765299.2023.2286713Backward bifurcation on HIV/AIDS SEI1I2TAR model with multiple interactions between sub-populationsUmmu Habibah0Trisilowati1Tiara Rizki Tania2Labib Umam Al-Faruq3Mathematics Department, Brawijaya University, Jl. Veteran Malang, East Java, IndonesiaMathematics Department, Brawijaya University, Jl. Veteran Malang, East Java, IndonesiaMathematics Department, Brawijaya University, Jl. Veteran Malang, East Java, IndonesiaMathematics Department, Brawijaya University, Jl. Veteran Malang, East Java, IndonesiaAbstractThe HIV/AIDS model was dynamically analyzed in this study. The model has seven compartments: the uneducated, the educated, the HIV-positive who take antiretroviral therapy (ART), the HIV-positive who do not take ART, people receiving ART treatment, people with AIDS who do not receive any treatment (full-blown AIDS), and the recovered. This model takes into account the analysis of the multiple interactions between the uneducated and the educated subpopulations, the HIV-positive who take and who do not take ART. The free-disease and endemic equilibrium points, as well as the basic reproduction number [Formula: see text] as a limit condition for infection-free and endemic occurrence, were produced by a mathematical analysis. The center-manifold hypothesis was used to prove that a backward bifurcation exists. The free-disease and endemic equilibrium points coexist when [Formula: see text] This means that HIV/AIDS is still spreading. A basic reproduction number below one is insufficient to constitute a free-disease condition. In order to determine essential parameters that significantly contribute to HIV/AIDS transmission, we computed sensitivity index values using a sensitivity analysis. The HIV/AIDS model and bifurcation parameter both identified the rate of HIV transmission from uneducated individuals to HIV-positive individuals who do not receive ART as the most crucial parameter. A numerical simulation supports the dynamical analysis.https://www.tandfonline.com/doi/10.1080/25765299.2023.2286713HIV/AIDS modeldynamical systemmultiple interactionsbackward bifurcation |
| spellingShingle | Ummu Habibah Trisilowati Tiara Rizki Tania Labib Umam Al-Faruq Backward bifurcation on HIV/AIDS SEI1I2TAR model with multiple interactions between sub-populations Arab Journal of Basic and Applied Sciences HIV/AIDS model dynamical system multiple interactions backward bifurcation |
| title | Backward bifurcation on HIV/AIDS SEI1I2TAR model with multiple interactions between sub-populations |
| title_full | Backward bifurcation on HIV/AIDS SEI1I2TAR model with multiple interactions between sub-populations |
| title_fullStr | Backward bifurcation on HIV/AIDS SEI1I2TAR model with multiple interactions between sub-populations |
| title_full_unstemmed | Backward bifurcation on HIV/AIDS SEI1I2TAR model with multiple interactions between sub-populations |
| title_short | Backward bifurcation on HIV/AIDS SEI1I2TAR model with multiple interactions between sub-populations |
| title_sort | backward bifurcation on hiv aids sei1i2tar model with multiple interactions between sub populations |
| topic | HIV/AIDS model dynamical system multiple interactions backward bifurcation |
| url | https://www.tandfonline.com/doi/10.1080/25765299.2023.2286713 |
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