Modelling the Nonlinear Incidence Rate of Drug Addiction: A Mathematical Approach

Drug addiction remains a critical public health issue impacting individuals and communities worldwide. This study presents a mathematical model designed to analyze the dynamics of drug addiction transmission within a population. The model features nonlinear incidence rates and categorizes the population into five compartments: susceptible, exposed, addicted, quarantined or rehabilitated, and recovered individuals. Key parameters influencing transmission and recovery processes are identified and examined, particularly intervention factors that reduce addiction spread. The basic reproduction number, , serves as a threshold determining the stability of equilibrium states. When , the drug-free equilibrium is stable, whereas indicates the persistence of addiction within the population. A forward bifurcation is observed at , signifying a critical transition point in the system’s dynamics where stability shifts between equilibria. The analysis highlights that preventive and rehabilitative interventions significantly influence the control of addiction prevalence. These findings offer valuable insights for designing effective public health strategies aimed at mitigating the drug addiction epidemic.