Analisis Model Matematika Susceptible–Exposed–Alcoholic–Recovered–Susceptible Penyebaran Kecanduan Alkohol pada Kalangan Remaja di Kota Makassar
DOI:
https://doi.org/10.30605/proximal.v9i3.9843Keywords:
Model matematika, SEARS, Kecanduan alkohol, Kestabilan titik kesetimbanganAbstract
Kecanduan alkohol pada remaja merupakan permasalahan sosial dan kesehatan masyarakat yang memerlukan pendekatan sistematis untuk mendukung upaya pencegahan dan penanganan. Penelitian ini bertujuan mengembangkan dan menganalisis model matematika SEARS (Susceptible–Exposed–Alcoholic–Recovered–Susceptible) untuk menggambarkan dinamika kecanduan alkohol pada remaja di Kota Makassar. Model dirumuskan dalam sistem persamaan diferensial dengan mempertimbangkan kemungkinan individu yang telah pulih kembali ke kelompok rentan. Analisis dilakukan melalui penentuan titik kesetimbangan, matriks Jacobian, kestabilan lokal berdasarkan nilai eigen, bilangan reproduksi dasar, dan simulasi numerik. Hasil menunjukkan bahwa titik kesetimbangan bebas kecanduan alkohol tidak stabil, sedangkan titik kesetimbangan endemik stabil asimtotik lokal. Simulasi memperlihatkan bahwa proporsi Susceptible meningkat dari 0,87 menjadi 0,95, Exposed menurun dari 0,05 menjadi 0,04, sedangkan Alcoholic dan Recovered menurun hingga mendekati nol berdasarkan parameter dan kondisi awal yang digunakan. Kebaruan penelitian ini terletak pada penerapan model SEARS yang mempertimbangkan kemungkinan kekambuhan atau kembalinya individu yang pulih ke kelompok rentan. Model ini diharapkan menjadi kerangka analitis awal bagi Pemerintah Kota Makassar dalam merumuskan kebijakan pencegahan melalui edukasi, penguatan lingkungan sosial yang mendukung perilaku sehat, serta peningkatan akses konseling dan rehabilitasi. Validasi menggunakan data empiris lokal dan analisis sensitivitas parameter diperlukan untuk meningkatkan keandalan model serta mengevaluasi efektivitas strategi intervensi.References
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Copyright (c) 2026 Zahrah Nuriramadhana Arief, Wahidah Sanusi, Alimuddin Tampa, Nur Insani Maiwa
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