About 15 years ago our cat brought fleas back from the cat sitter's house,
and indeed they liked to munch on humans too. The poor cat would have
to suffer a bath once a week in all those hartz flea dip stuff, fleas would
even crawl right accross her eyeball in the tub as I picked off several dozen
or more of the critters. After a few months of this, and wrecking the wood
floor with one of those flea traps with the light over it (don't put them over
a towel) we finally gave into "chemicals".
The one we used was a growth regulating hormone. I did not kill adult fleas,
just made is so their eggs would not hatch. By that time we were desperate
and sprayed it everywhere - all carpets, furnature... There were some warnings
to stay out while it dried, might have been more about the carrier liquid than
the hormone itself.
Worked - fleas were gone.
This is the same principal as some of the new flea treatments, which use the
same active ingrediant as some of the most effective termite treatments. It
is so non-lethal to mammals that your cat can eat it (early versions were given
as a pill I believe), but terribly lethal to insects.