Before revision:  In our semi-analytical model, we identified two distinct tipping points between controlled and uncontrolled spreading: one, at which the behavior-driven reproduction number of the hidden infections becomes too large to be compensated by the available TTI capabilities, and one at which the number of new infections starts to exceed the tracing capacity , causing a self-accelerating spread.
After revision:  In our semi-analytical model, we identified two distinct tipping points between controlled and uncontrolled spreading: one, at which the behavior-driven reproduction number of the hidden chains becomes too large to be compensated by the available TTI capabilities, and one at which the number of new infections starts to exceed the tracing capacity , causing a self-accelerating spread.