(a) Stability regions of (bottom-right region) and (upper-left region) at (δ, m) = (0.001, 0.0005) in the bistability region of figure 2, as they depend on κ and x(0). (b) Simulated vaccine coverage for κ = 2 yr−1 in the stability region of (dashed line) and κ = 3 yr−1 in the stability region of (solid line). Other parameter values are σ = 1, δ = 0.001, m = 0.0005, x(0) = 0.6, β = 280 yr−1, μ = 1/50 yr−1 and γ = 365/22 yr−1.