Given estimates of R 0 and s(0), we use equation (4.5) to obtain an estimate of this maximum serological attack rate ðâ max Þ, noting that this estimate is quite robust to a range of underlying spatial contact structures and variation in infective potential among individuals (Ma & Earn 2006) . In the second scenario, we assume that the eventual extinction of the epidemic is a result of the development of resistance in the wider community. The optimum attack rate is obtained by applying social distancing such that as the proportion of susceptibles in the community falls below 1/R 0 , the number of infectives is so small that the epidemic fades out without infecting a significant fraction of the remaining susceptible population. Here, the ultimate proportion of the population remaining susceptible is s(N)Z1/R 0 (if s(N)O1/R 0 , reintroduction of the infection could lead to another epidemic wave). This condition allows us to define a min Zs(0)K1/R 0 and, given estimates of R 0 and s(0), we can obtain an estimate of this minimum attack rate ðâ min Þ. One would think that achieving this limit in practice should be rather difficult due to its extreme nature.