Subthreshold domain of bistable equilibria for a model of HIV epidemiology

Abstract

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 (ℛ0) being less than unity is satisfied. It is shown that under specific conditions, the community-wide eradication of HIV is feasible ifℛ0<ℛ∗, whereℛ∗is some threshold quantity less than unity. Furthermore, for the bistability case (which occurs whenℛ∗<ℛ0<1), it is shown that HIV eradication is dependent on the initial sizes of the subpopulations of the model.