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The Impact of the Effectiveness of Needle Exchange Programs on Addiction-Treatment Dynamics

The aim of this research is to determine the impact of needle exchange programs as motivation for intravenous drug users to seek treatment for addiction. A mathematical model of the dynamics of a population of drug users that incorporates a needle exchange program is formulated. We define the basic addiction reproduction number for the proposed model and explore its role in the prevalence and control of needle-sharing drug addiction. Specifically, the local stability of the injection-addiction free and endemic equilibria are determined. Sensitivity analysis is conducted to determine the impact of perturbations of key parameters on the basic reproduction number and endemic level of the subpopulations. Results include a notable impact of the ineffectiveness of the needle exchange program on the proportion of the subpopulation in treatment. Furthermore, conditions necessary for an injection-addiction free population are determined.

Article Number:
MTBI-11-02M

Year:
2014

Authors:
Mayra Coronado – Regis University
Natalia de la Torre – Mary Baldwin College
Omari Gill Jr. – Clark Atlanta University
Aidan Grennell – Western Carolina University
Romarie Morales – Arizona State University
Aprillya Lanz – Norfolk State University
Muntaser Safan – Arizona State University

the_impact_of_the_effetiveness_of_needle_exchange_programs.pdf