Computational Study of a Fractional-Order HIV Epidemic Model with Latent Phase and Treatment
In this work, we propose and investigate a model of the dynamical behavior of HIV/AIDS transmission by considering a new compartment of the population with HIV: the latent asymptomatic class. The infection reproduction number that stabilizes the global dynamics of the model is evaluated. We analyze...
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MDPI AG
2025-01-01
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| Series: | Fractal and Fractional |
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| author | Sana Abdulkream Alharbi Nada A. Almuallem |
| author_facet | Sana Abdulkream Alharbi Nada A. Almuallem |
| author_sort | Sana Abdulkream Alharbi |
| collection | DOAJ |
| description | In this work, we propose and investigate a model of the dynamical behavior of HIV/AIDS transmission by considering a new compartment of the population with HIV: the latent asymptomatic class. The infection reproduction number that stabilizes the global dynamics of the model is evaluated. We analyze the model’s global asymptotic stability using the Lyapunov function and LaSalle’s invariance principle. To identify the primary factors affecting the dynamics of HIV/AIDS, a sensitivity analysis of the model parameters is conducted. We also examine a fractional-order HIV model using the Caputo fractional differential operator. Through qualitative analysis and applications, we determine the existence and uniqueness of the model’s solutions. We derive some results from the fixed-point theorem and Ulam–Hyers stability. Ultimately, the obtained numerical simulation results are in agreement with the analytical outcomes obtained from the model analysis. Our findings illustrate the efficacy of the fractional model in depicting the dynamics of the HIV/AIDS epidemic and offering critical insights for the formulation of effective control strategies. The results show that early intervention and treatment in the latent phase of infection can decrease the spread of the disease and its progression to AIDS, as well as increase the success of treatment strategies. |
| format | Article |
| id | doaj-art-c729f7be8f734b189ad53ac31538aced |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-c729f7be8f734b189ad53ac31538aced2025-01-24T13:33:25ZengMDPI AGFractal and Fractional2504-31102025-01-01912810.3390/fractalfract9010028Computational Study of a Fractional-Order HIV Epidemic Model with Latent Phase and TreatmentSana Abdulkream Alharbi0Nada A. Almuallem1Department of Mathematics & Statistics, College of Science, Taibah University, Yanbu 41911, Saudi ArabiaDepartment of Mathematics & Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi ArabiaIn this work, we propose and investigate a model of the dynamical behavior of HIV/AIDS transmission by considering a new compartment of the population with HIV: the latent asymptomatic class. The infection reproduction number that stabilizes the global dynamics of the model is evaluated. We analyze the model’s global asymptotic stability using the Lyapunov function and LaSalle’s invariance principle. To identify the primary factors affecting the dynamics of HIV/AIDS, a sensitivity analysis of the model parameters is conducted. We also examine a fractional-order HIV model using the Caputo fractional differential operator. Through qualitative analysis and applications, we determine the existence and uniqueness of the model’s solutions. We derive some results from the fixed-point theorem and Ulam–Hyers stability. Ultimately, the obtained numerical simulation results are in agreement with the analytical outcomes obtained from the model analysis. Our findings illustrate the efficacy of the fractional model in depicting the dynamics of the HIV/AIDS epidemic and offering critical insights for the formulation of effective control strategies. The results show that early intervention and treatment in the latent phase of infection can decrease the spread of the disease and its progression to AIDS, as well as increase the success of treatment strategies.https://www.mdpi.com/2504-3110/9/1/28asymptotic behavior HIV/AIDS dynamicsfractional HIV/AIDS modelingUlam–Hyers stabilitysensitivity analysis |
| spellingShingle | Sana Abdulkream Alharbi Nada A. Almuallem Computational Study of a Fractional-Order HIV Epidemic Model with Latent Phase and Treatment Fractal and Fractional asymptotic behavior HIV/AIDS dynamics fractional HIV/AIDS modeling Ulam–Hyers stability sensitivity analysis |
| title | Computational Study of a Fractional-Order HIV Epidemic Model with Latent Phase and Treatment |
| title_full | Computational Study of a Fractional-Order HIV Epidemic Model with Latent Phase and Treatment |
| title_fullStr | Computational Study of a Fractional-Order HIV Epidemic Model with Latent Phase and Treatment |
| title_full_unstemmed | Computational Study of a Fractional-Order HIV Epidemic Model with Latent Phase and Treatment |
| title_short | Computational Study of a Fractional-Order HIV Epidemic Model with Latent Phase and Treatment |
| title_sort | computational study of a fractional order hiv epidemic model with latent phase and treatment |
| topic | asymptotic behavior HIV/AIDS dynamics fractional HIV/AIDS modeling Ulam–Hyers stability sensitivity analysis |
| url | https://www.mdpi.com/2504-3110/9/1/28 |
| work_keys_str_mv | AT sanaabdulkreamalharbi computationalstudyofafractionalorderhivepidemicmodelwithlatentphaseandtreatment AT nadaaalmuallem computationalstudyofafractionalorderhivepidemicmodelwithlatentphaseandtreatment |