High impact epidemics constitute one of the largest threats humanity is facing in the 21^st century. In the absence of pharmaceutical interventions, physical distancing together with testing, contact tracing and quarantining are crucial in slowing down epidemic dynamics. Yet, here we show that if testing capacities are limited, containment may fail dramatically because such combined countermeasures drastically change the rules of the epidemic transition: Instead of continuous, the response to countermeasures becomes discontinuous. Rather than following the conventional exponential growth, the outbreak that is initially strongly suppressed eventually accelerates and scales faster than exponential during an explosive growth 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.

高影响力流行病是人类在21^世纪面临的最大威胁之一世纪。在没有药物干预的情况下，物理疏远以及测试，接触者追踪和隔离对减缓流行病动态至关重要。然而，在这里我们表明，如果测试能力受到限制，则遏制可能会失败，因为这样的组合对策会极大地改变流行病转变的规则：对策的响应不是连续的，而是不连续的。最初的爆发被强烈抑制，而不是遵循常规的指数增长，最终在爆发性增长时期比指数增长更快并扩大规模。结果，遏制措施要么足以在总病例数较低的情况下阻止爆发，要么在略微太弱的情况下灾难性地失败，