In our last house, the bad heating meant that we didn't really have a flea problem in winter. The fleas you catch on your cat are probably not all of the fleas which are on your cat. The fleas which are on your cat represent a measly 5 per cent of your total house flea population. Call that 100 fleas per cat to make the sums easier. No wonder the people were getting bitten as well as the cats.
Fleas breed faster in warmer weather.
She was too young to use any of the things you could get then which you can apply to the cat. She is, and was, allergic to flea bites. This worked, but it was time consuming and it only got rid of what was on the cat, when the cat would condescend to be combed. It was a considerable relief when the cat reached the age of insecticide-tolerance and the weather got cooler. Frontline is, itself, an excellent flea control product.