Numerical Solution of Drug Addiction Mathematical Model Using Adams Moulton Method - Nurul Ismi Maulida; Syafruddin Side; Rahmat Syam (Jurusan Matematika FMIPA Universitas Pattimura, 2025)
Rug abuse is one of the major social issues in Indonesia, particularly in South Sulawesi. This study aims to develop a mathematical model that represents the dynamics of drug addiction in the population and to solve the model numerically using the Adams-Moulton method. The model applied is theSIIHRcompartment model, which segments the population into five groups: susceptible (S), light addict (IR), heavy addict (IB), in rehabilitation (H), and recovered (R). The analysis results indicate that the basic reproduction number푅₀is less than 1, suggesting that drug addiction in the population can be managed. Numerical simulations are conducted using the fifth-orderRunge-Kuttamethod for initial values, followed by theAdams-Bashforth-Moultonmethod as the numerical solution technique. The model demonstrates stability at the drug-free equilibrium point and consistency between the outcomes of mathematical and numerical analysis.