International Scholarly Research Network ISRN Biomathematics Volume 2012, Article ID 919502, 17 pages doi:10.5402/2012/919502 Research Article A Mathematical Model for Assessing the Impact of Intravenous Drug Misuse on the Dynamics of HIV and HCV within Correctional Institutions S. Mushayabasa, Claver P. Bhunu, and Alexander G. R. Stewart Department of Mathematics, University of Zimbabwe, P.O. Box MP 167, Harare, Zimbabwe Correspondence should be addressed to S. Mushayabasa, steadymushaya@gmail.com 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. 1. Introduction Prior studies suggests that prevalence of both human immunodeficiency virus (HIV) and hepatitis C virus (HCV) infections is known to be higher among incarcerated populations than the general population, since a high proportion of incarcerated individuals originate from high- risk environments and have high-risk behaviors, especially drug use [1–6]. HCV and HIV coinfections represent a public health problem of growing importance; because of similar modes of spread, many people are coinfected with HCV and HIV or HCV and HBV and in some cases with all three viruses at the same time [5]. In particular, HCV/HIV coinfections are common and are known as “twin epidemics” [6, 7]. Both HIV and HIV are blood born RNA (ribonu- cleic acid) viruses that replicate rapidly. Unsafe injecting practices, blood exchange and the use of non-sterile needles are the most efficient means of transmitting both viruses [6, 8]. Correctional institutions host a disproportionately high prevalence of HCV infection and coinfections. The preva- lence of HCV among prisoners approaches 57.5% and far exceeds that of HIV in prison [9, 10]. Transmission of these infections is believed to be a rare consequence of blood or body fluid exposures in the prison. However, if transmission does occur, the consequences are permanent and potentially fatal [5–7]. Coinfection with the two viruses (HCV/HIV) is associated with an accelerated course of hepatitis C disease [5–7]. Prison populations constitute a very high-risk group; they have high levels of HCV infection and HIV or HBV coinfection [11, 12]. HCV positive inmates are at exceptional risk for coinfection with HIV because of the association of injectable substance abuse [9–12]. Mathematical models have become invaluable manage- ment tools for epidemiologists, both shedding light on the mechanisms underlying the observed dynamics as well as making quantitative predictions on the effectiveness of different control measures. The literature and development