FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION
Drug abuse poses significant challenges to public health and socio-economic stability worldwide. Narcotics, which are psychotropic compounds, are typically used for treating specific medical conditions. Currently, many individuals abuse drugs outside of the function of treatment. This misuse leads t...
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| Format: | Article |
| Language: | English |
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Universitas Pattimura
2025-01-01
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| Series: | Barekeng |
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14594 |
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| author | Indah Nurun Izzati Fatmawati Fatmawati Cicik Alfiniyah |
| author_facet | Indah Nurun Izzati Fatmawati Fatmawati Cicik Alfiniyah |
| author_sort | Indah Nurun Izzati |
| collection | DOAJ |
| description | Drug abuse poses significant challenges to public health and socio-economic stability worldwide. Narcotics, which are psychotropic compounds, are typically used for treating specific medical conditions. Currently, many individuals abuse drugs outside of the function of treatment. This misuse leads to central nervous system disorders, resulting in significant mental and behavioral health issues. In this article, we discuss a fractional-order mathematical model for the transmission of drug users with fractional-order α∈ (0,1]. We employ fractional-order differential equations using the Caputo derivative approach to model the transmission dynamics. We analyze the local stability of drug-free and endemic equilibrium points and calculate the basic reproduction number (). Our analysis indicates that the drug-free equilibrium is locally asymptotically stable when , while the endemic equilibrium is stable when . We implement a numerical scheme to simulate the fractional-order model, illustrating the theoretical findings. |
| format | Article |
| id | doaj-art-ef5a30425f3144448035e6fe91f07abb |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-ef5a30425f3144448035e6fe91f07abb2025-08-20T03:41:56ZengUniversitas PattimuraBarekeng1978-72272615-30172025-01-0119151152410.30598/barekengvol19iss1pp511-52414594FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSIONIndah Nurun Izzati0Fatmawati Fatmawati1Cicik Alfiniyah2Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, IndonesiaDepartment of Mathematics, Faculty of Science and Technology, Universitas Airlangga, IndonesiaDepartment of Mathematics, Faculty of Science and Technology, Universitas Airlangga, IndonesiaDrug abuse poses significant challenges to public health and socio-economic stability worldwide. Narcotics, which are psychotropic compounds, are typically used for treating specific medical conditions. Currently, many individuals abuse drugs outside of the function of treatment. This misuse leads to central nervous system disorders, resulting in significant mental and behavioral health issues. In this article, we discuss a fractional-order mathematical model for the transmission of drug users with fractional-order α∈ (0,1]. We employ fractional-order differential equations using the Caputo derivative approach to model the transmission dynamics. We analyze the local stability of drug-free and endemic equilibrium points and calculate the basic reproduction number (). Our analysis indicates that the drug-free equilibrium is locally asymptotically stable when , while the endemic equilibrium is stable when . We implement a numerical scheme to simulate the fractional-order model, illustrating the theoretical findings.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14594drug usermathematical modelingcaputo derivativestability |
| spellingShingle | Indah Nurun Izzati Fatmawati Fatmawati Cicik Alfiniyah FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION Barekeng drug user mathematical modeling caputo derivative stability |
| title | FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION |
| title_full | FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION |
| title_fullStr | FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION |
| title_full_unstemmed | FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION |
| title_short | FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION |
| title_sort | fractional order model of the drug user transmission |
| topic | drug user mathematical modeling caputo derivative stability |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14594 |
| work_keys_str_mv | AT indahnurunizzati fractionalordermodelofthedrugusertransmission AT fatmawatifatmawati fractionalordermodelofthedrugusertransmission AT cicikalfiniyah fractionalordermodelofthedrugusertransmission |