Computational and Mathematical Methods in Medicine
Volume 2011 (2011), Article ID 846174, 15 pages
http://dx.doi.org/10.1155/2011/846174
Research Article

Modeling Schistosomiasis and HIV/AIDS Codynamics

S. Mushayabasa1 and C. P. Bhunu1,2

1Modelling Biomedical Systems Research Group, Department of Applied Mathematics, National University of Science and Technology, P.O. Box 939 Ascot, Bulawayo, Zimbabwe
2Department of Veterinary Medicine, University of Cambridge, Cambridge CB3 OES, UK

Received 1 March 2010; Accepted 11 September 2010

Academic Editor: Sivabal Sivaloganathan

Copyright © 2011 S. Mushayabasa and C. P. Bhunu. 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.

Abstract

We formulate a mathematical model for the cointeraction of schistosomiasis and HIV/AIDS in order to assess their synergistic relationship in the presence of therapeutic measures. Comprehensive mathematical techniques are used to analyze the model steady states. The disease-free equilibrium is shown to be locally asymptotically stable when the associated disease threshold parameter known as the basic reproduction number for the model is less than unity. Centre manifold theory is used to show that the schistosomiasis-only and HIV/AIDS-only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. The impact of schistosomiasis and its treatment on the dynamics of HIV/AIDS is also investigated. To illustrate the analytical results, numerical simulations using a set of reasonable parameter values are provided, and the results suggest that schistosomiasis treatment will always have a positive impact on the control of HIV/AIDS.