I think one of the reasons there were not many cats around is basically because they used to eat them. And once in a while the restaurant cat catches would pick up an kitty they could find and take them back again to the restaurant. I recall seeing cats in glass exhibits out leading of the restaurants. But somewhere within then and now they restricted eating felines. So cats are actually not on the menu and now there are pet cats everywhere. Many of them began in someone's house and acquired thrown away, since many are incredibly friendly. Also they have this thing about abdomen worms. And in those days China had not been as modern as now so abdominal worms would have been a problem. Fleas are not a really problem because they may have tile flooring surfaces and solid wood furniture.
If this attitude towards cats dates back generations the other can realize why historians say the Black color Death were only available in China. Where there are rats and no cats then the rats dominate and that could have been a precursor for the condition to get near to people. Now whenever i go back to China you may still find rats playing around however, not so many in the enclosure estates. There are several down by the river. Also they employ a efficient rubbish tidy up system that retains the towns very clean. Where I stay the rubbish is gathered everyday. That would also keep the rat people down. And with so many discarded cats playing around the rats don't possess much of a chance. I've never seen this but I believe the government picks up 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.