China and Korea are two Asian countries. There are other ones that didn't react that way, and it stopped in those as well.
Stories about lockdowns and aggressive tracking are viral in western media, but are overwhelmingly second-hand and largely anecdotal. Where are the primary sources documenting that the panicky methods were what led to their success? The one common denominator to all of Asia is hygiene. They all told people to wash their hands. And that works, IF people actually do it. That's well documented and is why it's foremost of the CDC and WHO's simple advice.
Inductive reasoning is essential to science. Speculation takes a back seat to already-observed events. The scary new event, Italy, is anomalous compared to nearly every other. It also happens to be one of the most strident "lockdown" cases. If anything, that should invite critique of their response, not calls to imitate it.