Do people from the EU going to the U.K. need to get their passport stamped? If so, I would imagine this is how they would stop these people from entering the US. I believe this is what was done initially in Asia (couldn’t go from say China to Korea then to the US).
No, I don't mean that people in EU could travel here. I mean that they could infect people in the UK and then those people would infect Americans.
Also, I believe Americans can still travel to the EU and then return, potentially with an infection. Why not just shut down international travel for 2-4 weeks and get rid of this thing. Anything that is done is going to hurt people economically. I think more drastic moves will limit the time period over which this will occur.