Stability Analysis of Mathematical Model of Drug Abuse Case Rehabilitation Program in East Java

Kamiran; Basuki Widodo; Nur Asiyah; Amirul Hakam

doi:10.1063/5.0181111

Stability Analysis of Mathematical Model of Drug Abuse Case Rehabilitation Program in East Java

Kamiran
, Basuki Widodo^*
, Nur Asiyah
, Amirul Hakam

^*Corresponding author for this work

Institut Teknologi Sepuluh Nopember

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

The case of drug abuse is still a chronic problem for many countries, including Indonesia. One of the actions taken by the government in dealing with drug abuse cases is a rehabilitation program for addicts. Therefore, it is necessary to construct a mathematical model to observe the dynamics of the rehabilitation program for drug abuse cases. The mathematical model for the rehabilitation program for drug abuse cases is constructed based on the SIR epidemic model. Furthermore, through stability analysis, it was found that the model is asymptotically stable around the drug-free equilibrium point (E₀) if R₀ < 1 and is asymptotically stable around the drug-endemic equilibrium point (E₁) if it meets the appropriate conditions obtained based on the Routh-Hurwitz criteria. The results of numerical simulations on the mathematical model of the rehabilitation program for drug abuse cases show that the more individuals who participate in the rehabilitation program, the faster the drug-free state will be obtained.

Original language	English
Title of host publication	AIP Conference Proceedings
Editors	Elly Pusporani, Nashrul Millah, Eva Hariyanti
Publisher	American Institute of Physics Inc.
Edition	1
ISBN (Electronic)	9780735447738
DOIs	https://doi.org/10.1063/5.0181111
Publication status	Published - 22 Dec 2023
Event	International Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022 - Hybrid, Surabaya, Indonesia Duration: 2 Oct 2022 → 3 Oct 2022

Publication series

Name	AIP Conference Proceedings
Number	1
Volume	2975
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022
Country/Territory	Indonesia
City	Hybrid, Surabaya
Period	2/10/22 → 3/10/22

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

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10.1063/5.0181111

Cite this

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title = "Stability Analysis of Mathematical Model of Drug Abuse Case Rehabilitation Program in East Java",

abstract = "The case of drug abuse is still a chronic problem for many countries, including Indonesia. One of the actions taken by the government in dealing with drug abuse cases is a rehabilitation program for addicts. Therefore, it is necessary to construct a mathematical model to observe the dynamics of the rehabilitation program for drug abuse cases. The mathematical model for the rehabilitation program for drug abuse cases is constructed based on the SIR epidemic model. Furthermore, through stability analysis, it was found that the model is asymptotically stable around the drug-free equilibrium point (E0) if R0 < 1 and is asymptotically stable around the drug-endemic equilibrium point (E1) if it meets the appropriate conditions obtained based on the Routh-Hurwitz criteria. The results of numerical simulations on the mathematical model of the rehabilitation program for drug abuse cases show that the more individuals who participate in the rehabilitation program, the faster the drug-free state will be obtained.",

author = "Kamiran and Basuki Widodo and Nur Asiyah and Amirul Hakam",

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language = "English",

series = "AIP Conference Proceedings",

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Kamiran, , Widodo, B , Asiyah, N & Hakam, A 2023, Stability Analysis of Mathematical Model of Drug Abuse Case Rehabilitation Program in East Java. in E Pusporani, N Millah & E Hariyanti (eds), AIP Conference Proceedings. 1 edn, 040004, AIP Conference Proceedings, no. 1, vol. 2975, American Institute of Physics Inc., International Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022, Hybrid, Surabaya, Indonesia, 2/10/22. https://doi.org/10.1063/5.0181111

Stability Analysis of Mathematical Model of Drug Abuse Case Rehabilitation Program in East Java. / Kamiran, ; Widodo, Basuki ; Asiyah, Nur et al.
AIP Conference Proceedings. ed. / Elly Pusporani; Nashrul Millah; Eva Hariyanti. 1. ed. American Institute of Physics Inc., 2023. 040004 (AIP Conference Proceedings; Vol. 2975, No. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Hakam, Amirul

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Y1 - 2023/12/22

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AB - The case of drug abuse is still a chronic problem for many countries, including Indonesia. One of the actions taken by the government in dealing with drug abuse cases is a rehabilitation program for addicts. Therefore, it is necessary to construct a mathematical model to observe the dynamics of the rehabilitation program for drug abuse cases. The mathematical model for the rehabilitation program for drug abuse cases is constructed based on the SIR epidemic model. Furthermore, through stability analysis, it was found that the model is asymptotically stable around the drug-free equilibrium point (E0) if R0 < 1 and is asymptotically stable around the drug-endemic equilibrium point (E1) if it meets the appropriate conditions obtained based on the Routh-Hurwitz criteria. The results of numerical simulations on the mathematical model of the rehabilitation program for drug abuse cases show that the more individuals who participate in the rehabilitation program, the faster the drug-free state will be obtained.

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T3 - AIP Conference Proceedings

BT - AIP Conference Proceedings

A2 - Pusporani, Elly

A2 - Millah, Nashrul

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Stability Analysis of Mathematical Model of Drug Abuse Case Rehabilitation Program in East Java

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