(a) Impact of shared contacts, F, on the effect of opinion clustering, Δ. Results are shown for different local thresholds: T = 0.1 (circles), T = 0.2 (crosses), T = unlimited (triangles). (b) Impact of amount of agreement between parents; c = 80 per cent and β is varied. Shown is the probability of an outbreak for F = 0.2 (grey) and F = 1 (black) and for agreement between parents of 0.68 (i.e. random vaccination, solid line), 0.75 (triangles) and 0.85 (circles); T = 0.2.