When or if this hits the US or elsewhere in Europe, and it becomes obvious that despite the quarantine in Italy, the virus still continued to spread, they will question the measures being taken. As time goes on, the West will become critical of government response and may be difficult to control.
In China when the government tells its citizens to do something, they just do it. They don't ask why. They don't deliberate on whether it's the correct choice. They simply follow the directions. In the West, everything is up for debate. People don't like to be told what to do.