Duration (a) and (b), the final size of the epidemic (c) and (d) and the net benefit (e) and (f) as a function of α for different numbers of long-range random links. Each point is the mean of 20 simulation runs with error bars showing ±1 standard deviation. Parameters: p = 0.25, q = 0.5, c = 0.05, and r
= 2. 20% corresponds to 3,000 links, 30% to 4,500 and 100% represents a fully random network.