International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 18908, 11 pages
Research Article

Comparison of Single-Stage and Staged Progression Models for HIV/AIDS Transmission

F. Baryarama and J. Y. T. Mugisha

Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda

Received 14 June 2007; Revised 8 September 2007; Accepted 7 November 2007

Academic Editor: Thomas P. Witelski

Copyright © 2007 F. Baryarama and J. Y. T. Mugisha. 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 single-staged (SS) model and a staged progression (SP) model for HIV/AIDS with the same variable contact rate over time were formulated. In both models, analytical expressions for the HIV prevalence were obtained. A comparison of the two models was undertaken. It is shown that prevalence projections from the SS model are lower than projections from the SP model up to and beyond the peak prevalence, although the SS model prevalence may be higher than that of the SP model much later in the epidemic. A switch from faster SP model prevalence changes to faster SS prevalence changes occurs beyond the SP model peak prevalence. Hence using the SS model underestimates HIV prevalence in the early stages of the epidemic but may overestimate prevalence in the declining HIV prevalence phase. Our comparison suggests that the SP model provides better prevalence projections than the SS model. Moreover, the extra parameters that would make the SP model appear difficult to implement may not be sought from national survey data but from existing HIV/AIDS literature.