As much as I have been following this (I now know more about respirators and PPE than I ever would have wanted to), I'm still not clear regarding the tests. Is it binary - you do/don't have the virus - or does it show the presence of anti-bodies .... which would indicate that you had the virus and have recovered.
The former is important in that you can isolate the ill, but those who don't have it today could get it tomorrow. Knowing that someone had it, and then recovered, would be a huge boost because they should be available to go back into the work force.
(on my earlier comment, it reminds me of 2001, when I learned far too much about jihads and the taliban, or 2008/9, when I learned far too much about mortgage-backed securities and credit default swaps!).