  High impact epidemics constitute one of the largest threats humanity is
facing in the 21st century. Testing, contact tracing and quarantining are
critical in slowing down epidemic dynamics, but may prove insufficient for
highly contagious diseases. In the absence of pharmaceutical interventions,
physical distancing measures remain as the last resort to avoid a widespread
outbreak. Here we show that such combined countermeasures drastically change
the rules of the epidemic transition if testing capacities are limited: Instead
of continuous the response to countermeasures becomes discontinuous and rather
than following the conventional exponential growth, the outbreak accelerates
and scales super-exponentially during an intermediate period. As a consequence,
containment measures either suffice to stop the outbreak at low total case
numbers or fail catastrophically if marginally too weak, thus implying large
uncertainties in reliably estimating overall epidemic dynamics, both during
initial phases and during second wave scenarios.
