Cat fleas do the biting, and around 95 per cent of the population in a house is not on the animal. It is eggs, larvae and pupae in the carpet pile, the gaps between floorboards and under the bed, which is why treating the pet alone never clears it. The pupae are the difficult part, since the cocoon shrugs off insecticide and can sit dormant for weeks.
So it runs in two passes. Carpets, rugs, subfloor, pet bedding and the outside run where the animal sleeps get treated, then you vacuum daily for a fortnight, because the vibration triggers the pupae to hatch early onto treated surfaces. Fleas run hard here from November through April, and an empty rental between tenants is the classic: no host for months, then the whole lot hatches at once.