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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 languageEnglish
Title of host publicationAIP Conference Proceedings
EditorsElly Pusporani, Nashrul Millah, Eva Hariyanti
PublisherAmerican Institute of Physics Inc.
Edition1
ISBN (Electronic)9780735447738
DOIs
Publication statusPublished - 22 Dec 2023
EventInternational Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022 - Hybrid, Surabaya, Indonesia
Duration: 2 Oct 20223 Oct 2022

Publication series

NameAIP Conference Proceedings
Number1
Volume2975
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022
Country/TerritoryIndonesia
CityHybrid, Surabaya
Period2/10/223/10/22

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