A vaccination campaign has to reach a high proportion of a population to work, because protection is partly collective: once enough people are immune, the infection cannot find a path from one susceptible person to the next. This means that the last few per cent matter more than their number suggests, and they are usually the hardest to reach — families who move, districts without clinics, and people who distrust the authorities running the programme. Campaigns are often judged on averages that hide exactly these gaps.