You might consider requiring tests of anyone who's been to an airport, or traveled, etc.
Hell....with smartphone metrics nowadays, you could link exact whereabouts for anyone with a phone to an area someone who was infectious had been around the same timeframe. Ergo, the woman in Sacramento who was diagnosed, we could track her travel in the area over the past week or more, and cross correlate with anyone else at risk, then push messages out to folks at risk to get a test. Either make that a voluntary test and as a heads up, or in some cases, mandatory if infection is almost certain.
But once this escapes into the general population, quarantines aren't going to make much sense anymore.