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Subthreshold domain of bistable equilibria for a model of HIV epidemiology. (English) Zbl 1031.92023
Summary: A homogeneously 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 ($$\mathcal{R}_0$$) being less than unity is satisfied. It is shown that under specific conditions, the community-wide eradication of HIV is feasible if $$\mathcal{R}_0<\mathcal{R}_*$$, where $$\mathcal{R}_*$$ is some threshold quantity less than unity. Furthermore, for the bistability case (which occurs when $$\mathcal{R}_*<\mathcal{R}_0<1$$), it is shown that HIV eradication is dependent on the initial sizes of the subpopulations of the model.

##### MSC:
 92D30 Epidemiology 37C75 Stability theory for smooth dynamical systems 37N25 Dynamical systems in biology 34D05 Asymptotic properties of solutions to ordinary differential equations 34D23 Global stability of solutions to ordinary differential equations
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