Here's the reddit thread where I am taking this information from and the relevant quote:
https://www.reddit.com/r/China_Flu/comments/febv3t/what_its_like_in_china_0306/
"Public areas would take your name and phone number before allowing you to enter, in the event someone there later was determined positive, they could contact you and find you quickly. This moved digitally in QR code based systems, were you would scan various locations, buses, taxis, subways, etc. and be able to be contacted and located quickly."
This seems to be part of the containment infrastructure that China has deployed and it's working. South Korea appears to have a similar system, texting people who have been near someone who was infected. But I'm not sure about its exact operation, it might triangulate people's positions somehow. No idea.
Basically it's coronavirus Foursquare.
Since the US (and other governments) are not acting speedily on this, and it appears to be one the main ways to contain the outbreak, how realistic would it be for someone to build one and share it? I can imagine people would be willing to pay for it, and the QR code system could simply be made by volunteers and businesses who would stick it to the walls. I'd think people would flock to those businesses because they would feel safer.
As far as infections go, People could also self-report for the covid19 infection when they had it confirmed. Unfortunately, this is in no way a substitute for a proper government system, but I am pondering on how realistic this could be and how it could be made.