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
Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2, Manitoba, Canada
Received 20 September 2002
Copyright © 2003 B. D. Corbett 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.
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 () being less than unity is satisfied.
It is shown that under specific conditions, the community-wide
eradication of HIV is feasible if ,
where is some threshold quantity less than unity.
Furthermore, for the bistability case (which occurs when
), it is shown that HIV
eradication is dependent on the initial sizes of the
subpopulations of the model.