The benefit arising from interventions that additionally decrease R beyond that expected based on herd immunity alone may differ depending on the magnitude of the decrease and its timing (Bootsma & Ferguson 2007; Hatchett et al. 2007 ). If a reduction in the infectious contact rate can be introduced early and sustained, the overall attack rate can be reduced. For a given decrease in the contact rate, the relative reduction in the attack rate is smaller for larger R 0 (figure 1). For example, halving the infectious contact rate may lead to a major epidemic being averted (i.e. a 100% reduction in the attack rate) when R 0 Z2, but, at most, approximately only a 20% reduction in the attack rate if R 0 Z4 (figure 1).