A little more detail on what will happen when testing begins in earnest.
Patient A finally gets tested and they are positive. Then the health care professional ask questions and find out where they have been, who they have contacted etc.
Folks from their home, workplace are brought in for testing.
Some of them test positive.
Rinse and repeat in an exponential fashion until everyone in the test lab passes out from exhaustion or they run out of testing kits, whichever happens first.
Here’s a pretty good article largely about the China experience:
https://www.boston.com/news/health/2020/03/03/who-is-getting-coronavirus