I think one of the reasons there were few cats around is because they used to eat them. And once in a while the restaurant feline catches would grab an feline they may find and take them back again to the restaurant. I recall seeing pet cats in glass exhibits out leading of the restaurants. But somewhere within then and now they suspended eating pet cats. So cats are actually not on the menu and now there are pet cats everywhere. Many of them started off in someone's house and got thrown away, as most are very friendly. Also they have got this thing about belly worms. And in those days China had not been as modern as now so tummy worms would have been a problem. Fleas aren't really a problem because they have tile surfaces and real wood furniture.
Then your nine lives of the humble feline who only wished to help mankind by eliminating rodents that taken disease took a significant move for the more serious during the dark ages. Where witch hunts and losing at the stake were typical. Somebody who didn't like cats somehow connected them to witches plus they were burnt at the stake with there owners. The way they made that connection I'll never know. It began with Pope Gregory IX in the 1232 who deemed the normal house feline as diabolical. Then to make issues more serious in1484 along came the greatest feline killer ever, Pope Innocent VIII, who decreed something along the lines of all cats came from hell and really should came back to the fires of hell by fireplace. Felines were mercilessly prosecuted and were burnt so they would go back to the fires of hell. It is amazing any survived because if you were trapped with a kitty you were burnt along. I still go to chapel and sometimes I just wonder why. And of course the Black Death was in the backdrop surviving and growing because there were no pet cats to kill the rats that transported the fleas that induced the disease. Then along came the cat's savior King Louis XIII of France, who in the 1630s repealed the law and cats once again started to live. But they were still hated and killed for many centuries from then on. I don't know if the African american Death subsided but pet cats once again safeguarded mankind contrary to the diseases transported by rodents. Plus the famines brought on by mice plagues.