How about we start with every survivor on the floating petri dish called the Diamond Princess?
3700 passengers, 712 tested positive, the remaining ~3000 tested negative. Let's test them and get a good picture of what happens in a close quarter environment.
BTW, I work in a hospital laboratory where we would be performing these tests. The are not expensive, kind of like a home pregnancy test.
People who develop immunity do NOT NEED A VACCINE!