I'm fairly certain that Constitutional speaking "interstate commerce" can only be regulated by the federal government. The free movement of people may not be commerce per se, but it is inextricably linked.

In realpolitik terms, I doubt the federal government can stop this. What are they going to do? Send the army to force states to accept potentially infected people? That's basically an order to go kill your countrymen. I'd hope, given such an order, much of the military would defect.

The states also have their own well-equipped militias (National Guard). The U.S. Army can't just roll in and occupy a state if the state does not want it to - they will have to wage a war. Not at all politically acceptable.

With sufficient testing capabilities, closing the borders might not be necessary. Instead, test at the borders (and airports) and impose a mandatory quarantine on any infected individuals.

"California's got another Flu blockade up this week."