The effects of backward bifurcations. Solid curves indicate stable equilibria, while dashed curves indicate unstable equilibria. (a) A backward bifurcation at may result in persistence of the disease when . There is a point such that the endemic equilibrium exists for and a third, unstable, equilibrium also exists. Hence, the disease-free equilibrium is only globally stable if . (b) Backward bifurcations at other points may also affect the outcome. Although the disease persists for all and is eradicated when (due to the transcritical bifurcation at ), there is a region , where three equilibria coexist. In this region, the outcome depends on the initial conditions.
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