Pemodelan Matematika Pada Kecanduan Alkohol

Jihan Fikri Rasyidah, Juhari Juhari, Abdul Aziz

Abstract


 

Penelitian ini bertujuan untuk memodelkan dinamika kecanduan alkohol menggunakan pendekatan matematika dengan memodifikasi model SED (Susceptible-Exposed-Dependent) yang dikembangkan oleh Pérez Reyes (2020) dengan menambahkan kompartemen Recovery (R). Penambahan ini memungkinkan analisis yang lebih komprehensif tentang proses pemulihan dan potensi kekambuhan. Model dianalisis menggunakan transformasi proporsi populasi, analisis titik ekuilibrium, perhitungan bilangan reproduksi dasar, analisis sensitivitas parameter, dan simulasi numerik. Hasilnya menunjukkan bahwa nilai , menunjukkan bahwa sistem stabil secara asimtotik lokal pada titik ekuilibrium bebas kecanduan. Analisis sensitivitas menunjukkan bahwa parameter yang paling berpengaruh pada penyebaran kecanduan adalah tingkat interaksi antara individu yang rentan dan terpapar Simulasi numerik mendukung analisis teoritis dengan menunjukkan bahwa proporsi pecandu dan individu yang terpapar menurun seiring waktu, sementara proporsi individu yang rentan mendominasi dalam jangka panjang. Integrasi nilai-nilai Islam dalam penelitian ini memberikan pendekatan kontekstual terhadap pencegahan kecanduan alkohol di masyarakat.


Keywords


Kecanduan alkohol, model matematika, bilangan reproduksi dasar

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References


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DOI: https://doi.org/10.18860/jrmm.v4i6.34690

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