I think one of the reasons 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 feline 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 today they prohibited eating felines. So cats are now not on the menu and now there are felines everywhere. Most of them started off in someone's house and received thrown away, as most are incredibly friendly. Also they have this thing about tummy worms. And in those times China had not been as modern as now so abdomen worms is a problem. Fleas aren't a really problem because they have got tile surfaces and solid wood furniture.
Then the nine lives of the humble pet cat who only wanted to help mankind by getting rid of rodents that carried disease took a significant move for the worse during the dark ages. Where witch hunts and burning at the stake were the norm. Somebody who didn't like pet cats somehow connected these to witches and they were burnt at the stake with there owners. The way they made that connection I'll never know. It started off with Pope Gregory IX in the 1232 who regarded the common house kitten as diabolical. Then to make concerns worse in1484 along came the greatest cat killer of all time, Pope Innocent VIII, who decreed something such as all cats originated from hell and should returned to the fires of hell by flames. 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 caught with a feline you were burnt along. I still go to cathedral and sometimes I simply wonder why. And of course the Black Fatality was in the backdrop surviving and thriving because there have been no felines to kill the rats that taken the fleas that triggered the disease. Then along arrived the cat's savior Ruler Louis XIII of France, who in the 1630s repealed regulations and cats once more started to live. However they were still hated and killed for many generations from then on. I don't know if the Dark colored Fatality subsided but pet cats once again safeguarded mankind up against the diseases transported by rodents. Along with the famines brought on by mice plagues.