Kontrol Optimal Model Matematika Dinamika Korupsi dengan Pemberian Edukasi dan Kampanye, Perbaikan Sistem, dan Represif
Abstract
Salah satu masalah yang menarik untuk dikaji melalui pendekatan model matematika yaitu perilaku korupsi yang mengancam kehidupan masyarakat. Sektor pelayanan publik merupakan salah satu contoh lahan basah terkait korupsi birokrasi. Selain itu, adapula korupsi yang lebih besar karena mencakup pembuatan kebijakan politik. Pengembangan model dalam artikel ini dilakukan berdasarkan model matematika korupsi yang telah dikembangkan oleh (Fantaye dan Birhanu, 2021) dengan membagi populasi menjadi lima kompartemen yaitu susceptible (S), exposed (E), corrupt (C), jailed (J) dan honest (H). Penelitian ini bertujuan untuk menganalisis titik kesetimbangan pada model matematika dinamika korupsi serta memberikan penerapan kontrol optimal pada dinamika korupsi melalui strategi yang telah diusung oleh KPK yaitu edukasi dan kampanye, perbaikan sistem, dan strategi represif diharapkan mampu menangani kasus korupsi secara efektif. Dari hasil analisis model diperoleh dua titik kesetimbangan yaitu titik kesetimbangan tanpa korupsi dan titik kesetimbangan adanya korupsi. Titik kesetimbangan tersebut akan stabil jika memenuhi syarat yang ditetapkan oleh aturan Routh-Hurwitz. Berdasarkan hasil simulasi numerik, menunjukkan bahwa peran KPK dalam memberantas korupsi dengan edukasi dan kampanye, perbaikan sistem, dan strategi represif memberikan hasil yang efektif.
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