Cat fleas do the biting, and roughly 95 per cent of the population in a house is not on the animal at all. It is eggs, larvae and pupae down in the carpet pile, between floorboards and under the bed, which is why treating the pet alone never clears it. The pupae are the hard part, since the cocoon shrugs off insecticide and can sit dormant for weeks.
That dormancy is why holiday houses catch people out. A place shut up for months with no host, then a family walks in at Christmas and the whole lot hatches at once, triggered by warmth and vibration. The job runs in two passes with daily vacuuming in between, which brings the pupae out early onto treated surfaces.
