Table of Contents
ISRN Biomathematics
Volume 2012, Article ID 919502, 17 pages
Research Article

A Mathematical Model for Assessing the Impact of Intravenous Drug Misuse on the Dynamics of HIV and HCV within Correctional Institutions

Department of Mathematics, University of Zimbabwe, P.O. Box MP 167, Harare, Zimbabwe

Received 22 October 2012; Accepted 7 November 2012

Academic Editors: M. T. Figge and W. Raffelsberger

Copyright © 2012 S. Mushayabasa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Unsafe injecting practices, blood exchange, the use of nonsterile needles, and other cutting instruments for tattooing are common in correctional institutions, resulting in a number of blood transmitted infections. A mathematical model for assessing the dynamics of HCV and HIV coinfection within correctional institutions is proposed and comprehensively analyzed. The HCV-only and HIV-only submodels are first considered. Analytical expressions for the threshold parameter in each submodel and the cointeraction are derived. Global dynamics of this coinfection shows that whenever the threshold parameter for the respective submodels and the coinfection model is less than unity, then the epidemics die out, the reverse condition implies disease persistence within correctional institutions. Numerical simulations using a set of plausible parameter values are provided to support analytical findings.