Analysis of illegal drug transmission model using fractional delay differential equations
The global burden of illegal drug-related death and disability continues to be a public health threat in developed and developing countries. Hence, a fractional-order mathematical modeling approach is presented in this study to examine the consequences of illegal drug usage in the community. Based o...
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| Format: | Article |
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AIMS Press
2022
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| Online Access: | http://eprints.intimal.edu.my/1712/ |
| _version_ | 1848766813749379072 |
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| author | Komal, Bansal Trilok, Mathur Narinderjit Singh, Sawaran Singh Shivi, Agarwal |
| author_facet | Komal, Bansal Trilok, Mathur Narinderjit Singh, Sawaran Singh Shivi, Agarwal |
| author_sort | Komal, Bansal |
| building | INTI Institutional Repository |
| collection | Online Access |
| description | The global burden of illegal drug-related death and disability continues to be a public health threat in developed and developing countries. Hence, a fractional-order mathematical modeling approach is presented in this study to examine the consequences of illegal drug usage in the community. Based on epidemiological principles, the transmission mechanism is the social interaction between susceptible and illegal drug users. A pandemic threshold value (Λ) is provided for the illegal drug-using profession, which determines the stability of the model. The Lyapunov function is employed to determine the stability conditions of illegal drug addiction equilibrium point of society. Finally, the proposed model has been extended to include time lag in the delayed illegal drug transmission model. The characteristic equation of the endemic equilibrium establishes a set of appropriate conditions for ensuring local stability and the development of a Hopf bifurcation of the model. Finally, numerical simulations are performed to support the analytical results. |
| first_indexed | 2025-11-14T11:57:07Z |
| format | Article |
| id | intimal-1712 |
| institution | INTI International University |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:57:07Z |
| publishDate | 2022 |
| publisher | AIMS Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | intimal-17122023-01-17T05:32:10Z http://eprints.intimal.edu.my/1712/ Analysis of illegal drug transmission model using fractional delay differential equations Komal, Bansal Trilok, Mathur Narinderjit Singh, Sawaran Singh Shivi, Agarwal Q Science (General) QA75 Electronic computers. Computer science QA76 Computer software The global burden of illegal drug-related death and disability continues to be a public health threat in developed and developing countries. Hence, a fractional-order mathematical modeling approach is presented in this study to examine the consequences of illegal drug usage in the community. Based on epidemiological principles, the transmission mechanism is the social interaction between susceptible and illegal drug users. A pandemic threshold value (Λ) is provided for the illegal drug-using profession, which determines the stability of the model. The Lyapunov function is employed to determine the stability conditions of illegal drug addiction equilibrium point of society. Finally, the proposed model has been extended to include time lag in the delayed illegal drug transmission model. The characteristic equation of the endemic equilibrium establishes a set of appropriate conditions for ensuring local stability and the development of a Hopf bifurcation of the model. Finally, numerical simulations are performed to support the analytical results. AIMS Press 2022 Article PeerReviewed Komal, Bansal and Trilok, Mathur and Narinderjit Singh, Sawaran Singh and Shivi, Agarwal (2022) Analysis of illegal drug transmission model using fractional delay differential equations. AIMS Mathematics, 7 (10). pp. 18173-18193. ISSN 2473-6988 https://www.aimspress.com/article/doi/10.3934/math.20221000 |
| spellingShingle | Q Science (General) QA75 Electronic computers. Computer science QA76 Computer software Komal, Bansal Trilok, Mathur Narinderjit Singh, Sawaran Singh Shivi, Agarwal Analysis of illegal drug transmission model using fractional delay differential equations |
| title | Analysis of illegal drug transmission model using fractional delay differential equations |
| title_full | Analysis of illegal drug transmission model using fractional delay differential equations |
| title_fullStr | Analysis of illegal drug transmission model using fractional delay differential equations |
| title_full_unstemmed | Analysis of illegal drug transmission model using fractional delay differential equations |
| title_short | Analysis of illegal drug transmission model using fractional delay differential equations |
| title_sort | analysis of illegal drug transmission model using fractional delay differential equations |
| topic | Q Science (General) QA75 Electronic computers. Computer science QA76 Computer software |
| url | http://eprints.intimal.edu.my/1712/ http://eprints.intimal.edu.my/1712/ |