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All Journal Paradikma: Jurnal Pendidikan Matematika INSPIRATIF JURNAL PENDIDIKAN MATEMATIKA de Fermat : Jurnal Pendidikan Matematika MARISEKOLA: Jurnal Matematika Riset Edukasi dan Kolaborasi Issues in Mathematics Education (IMED) Cakrawala Venn: Journal of Sustainable Innovation on Education, Mathematics and Natural Sciences International Journal of Educational Research J-CEKI Issues in Mathematics Educations (IMED)
Rosauli Novalina Samosir
Universitas Negeri Manado
Arts Humanities Astronomy Chemistry Decision Sciences, Operations Research & Management Education Energy Environmental Science Materials Science & Nanotechnology Mathematics Physics Social Sciences Other

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Analysis of Vulnerable and Recovered Population Dynamics in the SAHTR Model Based on Variations in the Spread and Rehabilitation Rates Anggriani, Nita; Mangobi, James U.L.; Pratama, Muhammad Isbar; Samosir, Rosauli Novalina; Handayani, Lilis
Venn: Journal of Sustainable Innovation on Education, Mathematics and Natural Sciences Vol. 4 No. 3 (2025): Matematika, IPA, dan Pembelajarannya
Publisher : Pusat Studi Bahasa dan Publikasi Ilmiah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.53696/venn.v4i3.322

Abstract

Drug abuse continues to be a significant public health issue, especially in developing countries such as Indonesia, with increasing prevalence among the productive age group. This study develops and analyzes a compartmental mathematical model, SAHTR (Susceptible, Addicted-Lighter, Addicted-Heavier, Treatment, Recovery), using a nonlinear system of differential equations to simulate the dynamics of drug abuse spread and recovery. The model integrates an optimal control approach to evaluate the effectiveness of two intervention strategies: anti-drug campaigns and psychological counseling. Numerical simulations were carried out using the Runge-Kutta 4th order method, focusing on the sensitivity analysis of two key parameters: the rate of social transmission (β) and rehabilitation success rate (γ₂). The results show that while the β parameter influences the initial decline of the susceptible population, its long-term impact is relatively minimal. In contrast, the γ₂ parameter significantly affects the dynamics of the recovery compartment, indicating that improving rehabilitation efficiency can substantially reduce system burden and accelerate the return of individuals to a drug-free state. These findings suggest that intervention strategies should prioritize enhancing the quality and accessibility of rehabilitation programs, including structured therapy and post-recovery support. Moreover, social influence control alone is insufficient without being complemented by preventive and community-based approaches. Overall, this study contributes to evidence-based policymaking by demonstrating the value of mathematical modeling in understanding and combating drug abuse effectively.
Co-Authors Aisyiah Restutiningsih Putri Utami Anggriani, Nita Ermita Ermita Ermita Ermita Ermita Humuntal Banjarnahor Ichdar Domu Lauale, Arthur Zefanya Lilis Handayani Miftahul Jannah Muhammad Isbar Pratama Navel Oktaviandy Mangelep Nelwan, Andriani Waraney Pargaulan Siagian Philotheus E. A. Tuerah Vivian E. Regar