I think one of the reason why there were not many cats around is because they used to eat them. And once in a while the restaurant cat catches would grab an kitten they may find and take them back to the restaurant. I recall seeing cats in glass shows out leading of the restaurants. But somewhere within then and now they forbidden eating cats. So cats are actually not on the menu and today there are cats everywhere. Many of them started off in someone's house and got thrown away, since many are extremely friendly. Also they may have this thing about stomach worms. And in those days China had not been as modern as now so tummy worms would have been a problem. Fleas are not a really problem because they may have tile floor surfaces and real wood furniture.
If this frame of mind towards cats goes back generations the other can understand why historians say the Black Death started in China. Where there are rats and no cats then your rats dominate and that would have been a precursor for the condition to get near people. Now after i get back to China there are still rats running around however, not so many in the cover estates. There are plenty of down by the river. Also they employ a efficient rubbish tidy up system that will keep the cities very clean. Where I stay the rubbish is collected everyday. That could also keep carefully the rat population down. And with so many discarded cats running around the rats don't possess much of an opportunity. I've never seen this but I suspect the government accumulates a great deal of cats. There used to be colonies of stray cats living in some places however now I don't see them any longer.