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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 58, Pages 3679-3698

Subthreshold domain of bistable equilibria for a model of HIV epidemiology

Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada

Received 20 September 2002

Copyright © 2003 Hindawi Publishing Corporation. 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 homogeneous-mixing population model for HIV transmission, which incorporates an anti-HIV preventive vaccine, is studied qualitatively. The local and global stability analysis of the associated equilibria of the model reveals that the model can have multiple stable equilibria simultaneously. The epidemiological consequence of this (bistability) phenomenon is that the disease may still persist in the community even when the classical requirement of the basic reproductive number of infection (0) being less than unity is satisfied. It is shown that under specific conditions, the community-wide eradication of HIV is feasible if 0<, where is some threshold quantity less than unity. Furthermore, for the bistability case (which occurs when <0<1), it is shown that HIV eradication is dependent on the initial sizes of the subpopulations of the model.