Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 185939, 14 pages
Research Article

HIV/AIDS Model with Early Detection and Treatment

1General Studies Department, Arusha Technical College, P.O. Box 296, Arusha, Tanzania
2Mathematics Department, University of Dar es Salaam, P.O. Box 35062, Dar es Salaam, Tanzania

Received 21 December 2011; Accepted 23 January 2012

Academic Editors: G. Kyriacou and F. Lamnabhi-Lagarrigue

Copyright © 2012 Augustine S. Mbitila and Jean M. Tchuenche. 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.


A classical epidemiological framework is used to qualitatively assess the impact of early detection and treatment on the dynamics of HIV/AIDS. Within this theoretical framework, two classes of infected populations: those infected but unaware of their serological status and those who are aware of their disease status, are considered. In this context, we formulate and analyze a deterministic model for the transmission dynamics of HIV/AIDS and assess the potential population-level impact of early detection in curtailing the epidemic. A critical threshold parameter for which case detection will have a positive impact is derived. Model parameters sensitivity analysis indicates that the number of partners is the most sensitive (in increasing the average number of secondary transmission) parameter. However, the case detection coverage is the main drivers in reducing the initial disease transmission. Numerical simulations of the model are provided to support the analytical results. Early detection and treatment alone are insufficient to eliminate the disease, and other control strategies are to be explored.