Computational and Mathematical Methods in Medicine / 2011 / Article / Fig 5

Review Article

The Failure of 𝑅0

Figure 5

The effects of backward bifurcations. Solid curves indicate stable equilibria, while dashed curves indicate unstable equilibria. (a) A backward bifurcation at 𝑅 0 = 1 may result in persistence of the disease when 𝑅 0 < 1 . There is a point 𝑅 π‘Ž < 1 such that the endemic equilibrium exists for 𝑅 π‘Ž < 𝑅 0 < 1 and a third, unstable, equilibrium also exists. Hence, the disease-free equilibrium is only globally stable if 0 < 𝑅 0 < 𝑅 π‘Ž . (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 π‘š < 𝑅 0 < 𝑅 𝑛 , where three equilibria coexist. In this region, the outcome depends on the initial conditions.

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