COST EFFECTIVE APPROACH: OPTIMAL CONTROL APPLICATION IN NARCOTICS ABUSE MODEL BY INVOLVING THE NUMBER OF DEATHS - Thaibil Anwar; Eka Nurmala; Wahyudi; Sanusi; Sultan; Muhammad David (CV. Radja Publika, 2026)
Narcotics abuse represents a critical global public health challenge requiring strategic intervention through prevention and treatment mechanisms. This study addresses a significant gap in existing mathematical models of narcotics abuse by incorporating mortality as an explicit variable. While the foundational LH (Light user–Heavy user) model has been instrumental in understanding drug abuse dynamics, it fails to account for the substantial mortality burden associated with narcotics abuse. This research develops an extended LHD (Light user–Heavy user–Death) model by adding a death state to the original LH framework. The model is calibrated using data from Indonesia's National Narcotics Agency (BNN) through parameter selection that approximates observed trends. Optimal control theory is applied to minimize prevention and treatment budgets while maximizing intervention effectiveness. Simulations were conducted under three budget scenarios: unrestricted, restricted (Rp 735 billion based on 2014 allocation), and balanced (fifty–fifty allocation). Results demonstrate that prevention strategies dominate under unrestricted budget conditions, achieving a 78.8% reduction in light users, while treatment interventions become more prominent under budget constraints, with optimal resource allocation varying significantly across scenarios. The findings provide empirical evidence for evidence-based policy formulation in narcotics control programs and contribute methodologically to the field of mathematical epidemiology by explicitly modeling mortality dynamics in substance abuse.