Mathematical Modeling of Illicit Drug Use Dynamics Examining the Impact of Recycling Recovered Individuals into the Population.

Abstract

Illicit drug use continues to pose a significant threat to public health and societal well-being. This study aims to develop a comprehensive mathematical model that captures the dynamics of illicit drug use, considering different categories such as susceptible individuals, exposed individuals, drug addicts, and individuals in recovery. The model accounts for the fact that recovered individuals may not develop lifelong resistance to drugs and that those exposed to drug use cannot introduce new individuals into drug usage. Through the mathematical model, we seek to enhance our understanding of the behavior and patterns of illicit drug use, contributing valuable insights to the field of drug-related research. Additionally, the study explores the properties of the proposed model and utilizes the next generation matrix method to calculate the effective reproduction number. Furthermore, a sensitivity analysis is conducted to evaluate the impact of various parameters on the reproduction number, identifying the most effective control measures for mitigating the spread of drug-induced issues. The findings of this study serve as a warning indication to individuals and governments, emphasizing the need to intensify efforts in combating drug abuse. Moreover, the study highlights the importance of considering backward or forward bifurcation phenomena in determining the local stability of the model system at the endemic equilibrium point. This research contributes to the ongoing efforts to understand and address the complex challenges posed by illicit drug use, offering insights that can inform policies and  interventions aimed at curbing the spread of drug abuse and promoting overall community well-being.