Dynamical Analysis of a Fractional Order HIV/AIDS Model
This article discusses a dynamical analysis of the fractional-order model of HIV/AIDS. Biologically, the rate of subpopulation growth also depends on all previous conditions/memory effects. The dependency of the growth of subpopulations on the past conditions is considered by applying fractional der...
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| Format: | Article |
| Language: | English |
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Universitas Muhammadiyah Mataram
2021-04-01
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| Series: | JTAM (Jurnal Teori dan Aplikasi Matematika) |
| Subjects: | |
| Online Access: | http://journal.ummat.ac.id/index.php/jtam/article/view/3224 |
| _version_ | 1818919389296066560 |
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| author | Septiangga Van Nyek Perdana Putra Agus Suryanto Nur Shofianah |
| author_facet | Septiangga Van Nyek Perdana Putra Agus Suryanto Nur Shofianah |
| author_sort | Septiangga Van Nyek Perdana Putra |
| collection | DOAJ |
| description | This article discusses a dynamical analysis of the fractional-order model of HIV/AIDS. Biologically, the rate of subpopulation growth also depends on all previous conditions/memory effects. The dependency of the growth of subpopulations on the past conditions is considered by applying fractional derivatives. The model is assumed to consist of susceptible, HIV infected, HIV infected with treatment, resistance, and AIDS. The fractional-order model of HIV/AIDS with Caputo fractional-order derivative operators is constructed and then, the dynamical analysis is performed to determine the equilibrium points, local stability and global stability of the equilibrium points. The dynamical analysis results show that the model has two equilibrium points, namely the disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable when the basic reproduction number is less than one. The endemic equilibrium point exists if the basic reproduction number is more than one and is globally asymptotically stable unconditionally. To illustrate the dynamical analysis, we perform some numerical simulation using the Predictor-Corrector method. Numerical simulation results support the analytical results. |
| first_indexed | 2024-12-20T01:05:05Z |
| format | Article |
| id | doaj.art-d92d2290e6da414085913a8c7014c25f |
| institution | Directory Open Access Journal |
| issn | 2597-7512 2614-1175 |
| language | English |
| last_indexed | 2024-12-20T01:05:05Z |
| publishDate | 2021-04-01 |
| publisher | Universitas Muhammadiyah Mataram |
| record_format | Article |
| series | JTAM (Jurnal Teori dan Aplikasi Matematika) |
| spelling | doaj.art-d92d2290e6da414085913a8c7014c25f2022-12-21T19:58:53ZengUniversitas Muhammadiyah MataramJTAM (Jurnal Teori dan Aplikasi Matematika)2597-75122614-11752021-04-0151142710.31764/jtam.v5i1.32242462Dynamical Analysis of a Fractional Order HIV/AIDS ModelSeptiangga Van Nyek Perdana Putra0Agus Suryanto1Nur Shofianah2Brawijaya UniversityBrawijaya UniversityBrawijaya UniversityThis article discusses a dynamical analysis of the fractional-order model of HIV/AIDS. Biologically, the rate of subpopulation growth also depends on all previous conditions/memory effects. The dependency of the growth of subpopulations on the past conditions is considered by applying fractional derivatives. The model is assumed to consist of susceptible, HIV infected, HIV infected with treatment, resistance, and AIDS. The fractional-order model of HIV/AIDS with Caputo fractional-order derivative operators is constructed and then, the dynamical analysis is performed to determine the equilibrium points, local stability and global stability of the equilibrium points. The dynamical analysis results show that the model has two equilibrium points, namely the disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable when the basic reproduction number is less than one. The endemic equilibrium point exists if the basic reproduction number is more than one and is globally asymptotically stable unconditionally. To illustrate the dynamical analysis, we perform some numerical simulation using the Predictor-Corrector method. Numerical simulation results support the analytical results.http://journal.ummat.ac.id/index.php/jtam/article/view/3224fractional-orderpece methodhiv/aidsepidemic model |
| spellingShingle | Septiangga Van Nyek Perdana Putra Agus Suryanto Nur Shofianah Dynamical Analysis of a Fractional Order HIV/AIDS Model JTAM (Jurnal Teori dan Aplikasi Matematika) fractional-order pece method hiv/aids epidemic model |
| title | Dynamical Analysis of a Fractional Order HIV/AIDS Model |
| title_full | Dynamical Analysis of a Fractional Order HIV/AIDS Model |
| title_fullStr | Dynamical Analysis of a Fractional Order HIV/AIDS Model |
| title_full_unstemmed | Dynamical Analysis of a Fractional Order HIV/AIDS Model |
| title_short | Dynamical Analysis of a Fractional Order HIV/AIDS Model |
| title_sort | dynamical analysis of a fractional order hiv aids model |
| topic | fractional-order pece method hiv/aids epidemic model |
| url | http://journal.ummat.ac.id/index.php/jtam/article/view/3224 |
| work_keys_str_mv | AT septianggavannyekperdanaputra dynamicalanalysisofafractionalorderhivaidsmodel AT agussuryanto dynamicalanalysisofafractionalorderhivaidsmodel AT nurshofianah dynamicalanalysisofafractionalorderhivaidsmodel |