Dinamika dan kontrol optimal model perilaku kenakalan remaja dengan variasi jenis kenakalan

Rismawandi, Muhammad Rafi Dhaifullah (2025) Dinamika dan kontrol optimal model perilaku kenakalan remaja dengan variasi jenis kenakalan. Sarjana thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

INDONESIA: Kenakalan remaja sebagai fenomena sosial multidimensi telah menjadi perhatian utama dalam kajian psikologi sosial dan kesehatan masyarakat. Penelitian ini mengembangkan model matematika berbasis sistem persamaan diferensial nonlinear untuk menganalisis dinamika penyebaran perilaku kenakalan remaja dengan klasifikasi dua jenis kenakalan (pelanggar status dan kriminal) melalui pendekatan kompartemen yang membagi populasi remaja ke dalam empat kelompok populasi, dan merancang strategi kontrol optimal yang mengintegrasikan tiga bentuk intervensi terstruktur. Analisis kualitatif sistem dilakukan melalui pembuktian kepositifan dan keterbatasan, penentuan titik ekuilibrium bebas kenakalan (DFE) dan endemik beserta analisis stabilitasnya menggunakan metode Lyapunov, dan identifikasi adanya perilaku bifurkasi pada system serta penentuan jenis bifurkasinya. Sementara itu, formulasi kontrol optimal dikembangkan dengan menerapkan Prinsip Minimum Pontryagin yang menghasilkan sistem persamaan diferensial ordinier maju-mundur yang diselesaikan secara numerik menggunakan metode runge-kutta orde 4. Temuan ini tidak hanya memberikan kontribusi teoretis dalam pengembangan model epidemiologi sosial tetapi juga merekomendasikan kebijakan multisektoral berbasis bukti untuk program yang efektif dalam pengendalian kenakalan remaja yang dipengaruhi oleh interaksi sosial, dan berkelanjutan dengan memperhatikan aspek keadilan sosial dan efisiensi alokasi sumber daya. ENGLISH: : Juvenile delinquency as a multidimensional social phenomenon has become a major concern in social psychology and public health studies. This study develops a mathematical model based on a system of nonlinear differential equations to analyze the dynamics of the spread of juvenile delinquency behavior by classifying two types of delinquency (status offenders and criminals) through a compartmental approach that divides the juvenile population into four population groups, and designs an optimal control strategy that integrates three forms of structured interventions. Qualitative analysis of the system is carried out through proving positivity and limitations, determining delinquency-free and endemic equilibrium (DFE) points along with their stability analysis using the Lyapunov method, and identifying the presence of bifurcation behavior in the system and determining the type of bifurcation. Meanwhile, an optimal control formulation is developed by applying the Pontryagin Minimum Principle which produces a system of forward-backward ordinal differential equations that are solved numerically using the 4th order Runge-Kutta method. These findings not only provide theoretical contributions in the development of social epidemiological models but also recommend evidence-based multisectoral policies for effective programs in controlling juvenile delinquency that are influenced by social interactions, and sustainable by considering aspects of social justice and efficiency of resource allocation.

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