Kontrol Optimal Model Matematika pada Penyebaran Judi Online di Indonesia
DOI:
https://doi.org/10.30605/proximal.v9i4.9849Keywords:
Judi Online, Model SGQ, Kontrol Optimal, Edukasi Digital, Prinsip Minimum PontryaginAbstract
Penyebaran judi online di Indonesia memerlukan pendekatan pengendalian yang mempertimbangkan dinamika perilaku masyarakat dan sumber daya intervensi. Penelitian ini bertujuan menganalisis penerapan kontrol optimal berupa edukasi digital untuk mengurangi aktivitas judi online menggunakan model SGQ. Populasi dibagi menjadi tiga kelompok, yaitu individu rentan terlibat judi online , individu aktif berjudi , dan individu yang berhenti atau menghindari judi online . Model diselesaikan menggunakan metode forward-backward sweep dengan integrasi Runge–Kutta orde empat (RK4) selama 100 tahun. Kebaruan penelitian ini terletak pada pemodelan edukasi digital dengan efektivitas berbeda terhadap kelompok rentan dan kelompok aktif berjudi, sehingga strategi intervensi dapat dianalisis secara lebih spesifik. Hasil simulasi menunjukkan bahwa kontrol optimal mampu menekan puncak dan akumulasi proporsi individu aktif berjudi, dengan penurunan akumulasi sebesar 45.05% dibandingkan skenario tanpa kontrol. Intensitas intervensi optimal cenderung lebih tinggi pada awal periode dan menurun seiring waktu. Temuan ini menunjukkan bahwa edukasi digital berpotensi menjadi strategi pengendalian judi online, meskipun validasi menggunakan data empiris dan analisis sensitivitas lebih lanjut diperlukan untuk mendukung penerapannya dalam kebijakan.
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