The US never shut down travel from China, it banned people not from the US from traveling from China to the US. US citizens and some other groups were still allowed to travel.

Singapore started severely restrict travel and quarantining arriving citizens a couple days before the US ban.

https://www.gov.sg/article/how-is-singapore-limiting-the-spr...

A faster travel ban for Italy and other EU countries would have done the US more good.