MLB and the MLBPA have jointly released the results from the most recent batch of COVID-19/Coronavirus testing, which is for the week ending Thursday, July 16, 2020 (yesterday).
MLB says that of the 10,548 tests collected and sampled from people in the “Monitoring Testing” category — those who are not currently in the COVID-19 protocol due to a positive test or other issue — there were six new positive tests. Of those six, 5 were players and 1 was a staff member.
That is, I think, about as good a result as one could hope for, under the circumstances.