Model Matematika Susceptible–User–Recovered–Susceptible pada Dinamika Penyebaran Pengguna Narkoba di Sulawesi Selatan

Authors

DOI:

https://doi.org/10.30605/proximal.v9i3.9844

Keywords:

Model Matematika, Model SURS, Penyalahgunaan Narkoba, Bilangan Reporduksi Dasar, Simulasi Numerik

Abstract

Pemodelan dinamika penyalahgunaan narkoba di Sulawesi Selatan diperlukan untuk memahami kondisi yang memungkinkan pengguna terus bertambah meskipun proses pemulihan berlangsung. Penelitian ini bertujuan memformulasikan model SURS (Susceptible-User-Recovered-Susceptible), menentukan titik kesetimbangan, menganalisis kestabilan, menghitung bilangan reproduksi dasar, serta melakukan simulasi numerik. Penelitian menggunakan pendekatan pemodelan matematika dengan membagi populasi menjadi kelompok rentan, pengguna narkoba, dan pulih. Kondisi awal disusun menggunakan data BPS dan BNN serta asumsi, sedangkan parameter model bersumber dari penelitian terdahulu dan asumsi. Pada parameter yang digunakan, diperoleh titik kesetimbangan bebas pengguna narkoba (E0=(1,0,0)) dan titik kesetimbangan endemik (E1≈(0.889193,0.005385,0.105422)). Bilangan reproduksi dasar sebesar (R0≈1.125>1) menunjukkan bahwa pengguna narkoba dapat bertahan dalam sistem. Titik kesetimbangan bebas pengguna tidak stabil, sedangkan titik kesetimbangan endemik stabil asimptotik lokal. Simulasi numerik menunjukkan penurunan proporsi individu rentan serta peningkatan proporsi pengguna dan individu pulih selama periode simulasi. Hasil ini menunjukkan bahwa pemulihan dapat berlangsung bersamaan dengan bertambahnya pengguna. Oleh karena itu, upaya penanganan perlu mencakup pencegahan pengguna baru dan dukungan bagi individu yang telah pulih agar tidak kembali rentan terhadap penggunaan narkoba.

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Published

2026-10-20

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Vol. 9 No. 3 (2026): Volume 9 Nomor 3 Tahun 2026

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Copyright (c) 2026 Indo Tenri Angka, Alimuddin, Syafaruddin Side, Muh. Ishaq Firdaus

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How to Cite

Model Matematika Susceptible–User–Recovered–Susceptible pada Dinamika Penyebaran Pengguna Narkoba di Sulawesi Selatan. (2026). Proximal: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 9(3), 882-891. https://doi.org/10.30605/proximal.v9i3.9844