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In an attempt to understand the dynamics of substance abuse and forestall its potential spread in the population, a novel model based on nonlinear system of ordinary differential equations is formulated and analysed in this study. The model takes into account, among other important features, the influx of addicted immigrant and rehabilitation of individuals affected by substance abuse. Least squares method with minimization\u2010constrained function is employed to fit the model with the real data of substance\u2010induced mental cases under rehabilitation. Conditions that guarantee the existence and global asymptotic stability of steady states are established, and a key threshold quantity which measures the potential spread of substance abuse influence in a community comprising susceptible and prudent populations is determined. 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