A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative
In this paper, we are concerned with a deterministic Caputo fractional derivative mathematical model of HIV/AIDS with treatment and optimal control. We formulate a mathematical model that contains six compartments (including primary infection and treatment) and show that the model is well-posed. We...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/ijmm/9342227 |
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| author | Abdul-Aziz Hussein Benyam Mebrate |
| author_facet | Abdul-Aziz Hussein Benyam Mebrate |
| author_sort | Abdul-Aziz Hussein |
| collection | DOAJ |
| description | In this paper, we are concerned with a deterministic Caputo fractional derivative mathematical model of HIV/AIDS with treatment and optimal control. We formulate a mathematical model that contains six compartments (including primary infection and treatment) and show that the model is well-posed. We calculate the reproduction number and free and endemic equilibrium points. We prove the stability of free and endemic equilibrium points. The local stability is carried out by the linearization method, whereas the global stability is performed by Mittag–Leffler stability. We consider four control mechanisms and show their impact on the prevalence of HIV infection. Numerical solutions are performed using the optimal case of the two-stage explicit fractional order Runge–Kutta methods. |
| format | Article |
| id | doaj-art-cf686e58aee543b3a331dcc4482bb761 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cf686e58aee543b3a331dcc4482bb7612025-08-20T03:53:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252025-01-01202510.1155/ijmm/9342227A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo DerivativeAbdul-Aziz Hussein0Benyam Mebrate1Department of MathematicsDepartment of MathematicsIn this paper, we are concerned with a deterministic Caputo fractional derivative mathematical model of HIV/AIDS with treatment and optimal control. We formulate a mathematical model that contains six compartments (including primary infection and treatment) and show that the model is well-posed. We calculate the reproduction number and free and endemic equilibrium points. We prove the stability of free and endemic equilibrium points. The local stability is carried out by the linearization method, whereas the global stability is performed by Mittag–Leffler stability. We consider four control mechanisms and show their impact on the prevalence of HIV infection. Numerical solutions are performed using the optimal case of the two-stage explicit fractional order Runge–Kutta methods.http://dx.doi.org/10.1155/ijmm/9342227 |
| spellingShingle | Abdul-Aziz Hussein Benyam Mebrate A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative International Journal of Mathematics and Mathematical Sciences |
| title | A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative |
| title_full | A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative |
| title_fullStr | A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative |
| title_full_unstemmed | A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative |
| title_short | A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative |
| title_sort | fractional order model for hiv aids with treatment and optimal control using caputo derivative |
| url | http://dx.doi.org/10.1155/ijmm/9342227 |
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