Modelling Population Dynamics of Substance Abuse in the Presence of Addicted Immigrant With Real Data of Rehabilitation Cases

Excessive intake or injection of substances, namely, medications, alcohol, and other harmful drugs, has resulted into unimaginable serious consequences, including mental health and social problems. 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-constrained function is employed to fit the model with the real data of substance-induced 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. Sensitive parameters of the model are identified, and their effects on the dynamics of substance abuse transmission are investigated with a view to suggesting possible effective measures against the harmful spread of substance abuse in the population.