Mathematical Modeling and Sensitivity Analysis of Drug Abuse Dynamics with Awareness, Guidance & Counseling Interventions

Abstract

Drug abuse remains a major global public health and socioeconomic challenge, particularly among young people. This study develops a deterministic compartmental model to investigate the dynamics of drug addiction in a population under the influence of awareness programs, guidance and counseling and rehabilitation interventions. Qualitative analysis is conducted to establish the positivity of the model and determine the drug free equilibrium and the basic reproduction number R₀, which serves as a threshold for persistence or elimination of drug abuse. The results show that the drug free equilibrium is locally asymptotically stable when R₀, implying that drug addiction can be eradicated from the population. The endemic equilibrium representing the persistence of drug abuse is also derived and analyzed. Furthermore, sensitivity analysis is carried out and the result shows that Parameters with negative sensitivity indices indicate a reduction in the transmission of drug abuse as their values increase, while parameters with positive sensitivity indices signify an increase in the transmission potential when their values rise. Numerical simulations were carried out to validate the analytical findings and assess the effectiveness of intervention strategies.

DOI: https://doi.org/10.5281/zenodo.23123971