A "border check or control" is when they check somebody's ID (passport) to see if they are allowed into the country. Proving your ID does not stop a virus.
That is not a health check. If you have the right emergency quarantine regulations in place you can do this anywhere, that is precisely what the Italians are doing for the towns they have quarantined. It doesn't matter what your ID is, whether you are an Italian citizen or not, you aren't allowed out of the quarantine area. Nothing to do with border checks and nothing to do with Schengen, this is in the middle of a country.
And some countries have started doing temperature checks on all passengers flying in from certain countries.
I think what you are asking is are any countries doing health checks at land borders for people entering. So far no. And the Swiss have said it would be impractical on the Italian border, as 70,000 commuters cross from Italy into Switzerland every day, and back again in the evening.
That story Rab posted (here: https://community.ricksteves.com/travel-forum/italy/4-mar-2020-rome-embassy-alert-from-step-state-gov ) sounds a little suspicious.
"The Government of Italy has implemented enhanced screening and quarantine measures to reduce the spread of COVID-19. As of 12:00 AM March 3, all passengers on U.S.-bound flights whose temperature is higher than 99.5 degrees Fahrenheit are not being permitted to board."
Why would the Italian government put checks in place for passengers TO USA? Perhaps the US-Americans would put checks on landing passengers, as many countries have. But why would the Italians be concerned about protecting one country, and not others?
And the Italians would definitely not put a limit at "99.5 degrees Fahrenheit". I don't think any hospital in Italy would have thermometers marked in °F.
He hasn't posted a link to the story. Without that I don't believe it.
