Numerical Solution of Drug Addiction Mathematical Model Using Adams Moulton Method

Abstract

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.