This paper * suggested, under some pessimistic assumptions, that it would require "near-universal app usage and near perfect compliance" This is due to the large fraction of spread from asymptomatic/presymptomatic carriers.

My review of the paper is that their assumptions are overly optimistic and that contact tracing will be largely ineffective even at universal adoption.

* https://science.sciencemag.org/content/368/6491/eabb6936/tab...

https://twitter.com/adamvsteele/status/1259661260406349824?s...