Analyzing Campus Drug Abuse Dynamics Through an Infectious Disease Framework

This paper introduces a mathematical model to elucidate the transmission dynamics of drug abuse within a college environment, focusing on rehabilitation measures and recovery. By calculating the basic reproduction number R0 and integrating it with significant parameters for drug-free and drug-persistent equilibria, we reveal the nuanced impact of rehabilitation on the spread of drug abuse. Our findings indicate that the drug-free equilibrium of the model is locally asymptotically stable when R0 1. Numerical simulations demonstrate that increasing rehabilitation and recovery rates can reduce R0 below unity. However, the effectiveness of these measures may be influenced by factors such as the availability and type of rehabilitation facilities, the quality of rehabilitation programs, and social support systems for recovering students. Further analysis using contour plots highlights that effective control of drug abuse can be achieved with high rehabilitation and recovery rates. The sensitivity analysis of the parameters further underscores the importance of targeting interventions that reduce the transmission rate κ, such as preventive programs, awareness campaigns, or restrictions on access to drugs. In addition, the study proposes a combination of control strategies, including continuously recruiting a large portion of the infected student population into rehabilitation programs. Collectively, these measures offer promising approaches to managing and potentially eradicating drug abuse within college settings.