Currently, the US is testing about 250,000 per day, roughly a million per week. Redfield just said, in order to do effective contact tracing we need 40-50 million tests per month, 10-12 million per week. We have a long ways to go.
As far as test accuracy, the best test currently have about 5% false positives which means if you test 10 million people, 500,000 will show up as positive and require retesting. The number of false negatives is less simply because there are fewer actual infected people but that's still a significant problem. The false negatives are "walking grenades".
The false positives are not so much a problem because a false positive won't infect anyone but it gives a very misleading idea of how many people actually are infected. For instance, recently, New York did a sample using antibody testing which suggested that 10% of the people in New York had been infected, 21% in the City, 3% in the rural upstate but in fact almost all the positives could be explained by "false positives". So where does that leave any control strategy?
