Epidemic diseases afflict all countries, and all epidemics are costly to society. The present paper examines optimal vaccination trajectories before and after an outbreak of a special class of epidemics where the disease normally eradicates itself. The focus is on epidemics where mortality may be ignored, influenza being the prime example. One important insight is that there may be increasing returns to scale in vaccination. Copyright © 2011 John Wiley & Sons, Ltd.