I believe one of the reasons there were not many cats around is basically because they used to consume them. And once in a while the restaurant kitty catches would grab an pet cat they may find and take them back again to the restaurant. I recall seeing pet cats in glass exhibits out the front of the restaurants. But somewhere within then and today they prohibited eating felines. So cats are now not on the menu and now there are cats everywhere. Many of them started off in someone's house and got thrown away, as most are incredibly friendly. Also they have got this thing about abdominal worms. And in those times China was not as modern as now so stomach worms would have been a problem. Fleas are not a really problem because they have tile flooring and real wood furniture.
Cats and mankind have been moving into harmony for quite some time but that hasn't always been the situation. There were times when cats have been nearly destroyed in the name of God. And what took place the Black Death reigned supreme for a lot longer than it will. So we will go back to the origins of recorded record to enough time of the pharaohs of Egypt. Here cats were revered as Gods and many were mummified to last for eternity. As the felines guarded the grain warehouses and wiped out the rats and mice that fed on the grain. Therefore reducing famines, which were the curse of Egypt. It had been illegal to eliminate cats in those times, like cows in India today.