A backward bifurcation at R 0 = 1 may result in persistence of the disease when R 0 < 1. In this case, the disease will always persist for R 0 > 1. However, there is a point R a < 1 such that the endemic equilibrium exists for R a < R 0 < 1 and a third, unstable, equilibrium also exists between the two stable equilibria. Hence, an endemic disease is only eradicated if 0 < R 0 < R a . For R a < R 0 < 1, the outcome depends on initial conditions. If the disease is still in its early stages-that is, if the initial conditions are sufficiently small-then the system will approach the disease-free equilibrium and the disease will be eradicated. However, if the initial conditions are large, then the system will approach the endemic equilibrium and the disease will persist. Thus, a backward bifurcation prevents the system from switching to the disease-free equilibrium as soon as R 0 < 1 is reached. See Figure 5 (a). (a) A backward bifurcation at R 0 = 1 may result in persistence of the disease when R 0 < 1. There is a point R a < 1 such that the endemic equilibrium exists for R a < R 0 < 1 and a third, unstable, equilibrium also exists. Hence, the disease-free equilibrium is only globally stable if 0 < R 0 < R a . (b) Backward bifurcations at other points may also affect the outcome. Although the disease persists for all R 0 > 1 and is eradicated when R 0 < 1 (due to the transcritical bifurcation at R 0 = 1), there is a region R m < R 0 < R n , where three equilibria coexist. In this region, the outcome depends on the initial conditions.