We show that sub-spreading events, i.e. transmission events in which an infection propagates to few or no individuals, can be surprisingly important for defining the lifetime of an infectious disease epidemic and hence its waiting time to elimination or fade-out, measured from the time-point of its last observed case. While limiting super-spreading promotes more effective control when cases are growing, we find that when incidence is waning, curbing sub-spreading is more important for achieving reliable elimination of the epidemic. Controlling super-spreading in this low-transmissibility phase offers diminishing returns over non-selective, population-wide measures. By restricting sub-spreading, we efficiently dampen remaining variations among the reproduction numbers of infectious events, which minimizes the risk of premature and late end-of-epidemic declarations. Because case-ascertainment or reporting rates can be modelled in exactly the same way as control policies, we concurrently show that the under-reporting of sub-spreading events during waning phases will engender overconfident assessments of epidemic elimination. While controlling sub-spreading may not be easily realized, the likely neglecting of these events by surveillance systems could result in unexpectedly risky end-of-epidemic declarations. Super-spreading controls the size of the epidemic peak but sub-spreading mediates the variability of its tail.

我们表明，子传播事件，即感染传播到很少或没有个人的传播事件，对于定义传染病流行的生命周期及其等待消除或消失的等待时间可能非常重要，从其最后观察到的病例的时间点。虽然限制超级传播在病例增加时可以促进更有效的控制，但我们发现，当发病率下降时，遏制子传播对于实现可靠的流行病消除更为重要。在这个低传播阶段控制超级传播比非选择性的、全人群的措施收益递减。通过限制子传播，我们有效地抑制了传染事件的繁殖数量之间的剩余变化，这最大限度地减少了过早和延迟流行病结束宣布的风险。由于病例确定或报告率可以以与控制政策完全相同的方式建模，我们同时表明，在减弱阶段对子传播事件的报告不足将导致对流行病消除的评估过于自信。虽然控制子传播可能不容易实现，但监测系统可能忽视这些事件可能会导致意外危险的流行病结束声明。超传播控制流行高峰的大小，但次传播介导其尾部的可变性。我们同时表明，在衰退阶段对次传播事件的报告不足将导致对流行病消除的评估过于自信。虽然控制子传播可能不容易实现，但监测系统可能忽视这些事件可能会导致意外危险的流行病结束声明。超传播控制流行高峰的大小，但次传播介导其尾部的可变性。我们同时表明，在衰退阶段对次传播事件的报告不足将导致对流行病消除的评估过于自信。虽然控制子传播可能不容易实现，但监测系统可能忽视这些事件可能会导致意外危险的流行病结束声明。超传播控制流行高峰的大小，但次传播介导其尾部的可变性。