I believe one of the reason why there were not many cats around is because they used to eat them. And every now and then the restaurant kitty catches would pick up an pet cat they could find and take them back again to the restaurant. I remember seeing pet cats in glass displays out leading of the restaurants. But somewhere between then and now they forbidden eating felines. So cats are now not on the menu and today there are pet cats everywhere. Many of them began in someone's house and received thrown away, as most are extremely friendly. Also they have got this thing about belly worms. And in those times China was not as modern as now so abdominal worms would have been a problem. Fleas aren't a really problem because they may have tile surfaces and solid wood furniture.
Felines and mankind have been surviving in harmony for many years but that hasn't always been the case. There have been times when felines have been almost wiped out in the name of God. And what happened the Black Death reigned supreme for considerably longer than it will. So we will get back to the beginnings of recorded record to enough time of the pharaohs of Egypt. Here felines were revered as Gods and many were mummified to last for eternity. Because the cats guarded the grain warehouses and killed the rats and mice that fed on the grain. Therefore lowering famines, that were the curse of Egypt. It had been illegal to wipe out cats in those times, like cows in India today.