If an epidemic cannot be contained by social distancing, and goes on to infect a sizeable fraction, the serological attack rate a must lie between a minimum value a min and a maximum value a max . Consider two hypothetical major epidemics, the first without social distancing and the second with what we will argue is optimum effective social distancing. For an epidemic in a reasonably well-mixed population, unimpeded by social distancing, a max is obtained from R 0 and s(0) by the final size equation (Diekmann & Heesterbeek 2000) a max Z sð0Þð1Ke Ka max R 0 Þ: ð4:5Þ