论文标题
接触跟踪和簇隔离的流行病模型，以及检测悖论
A model for an epidemic with contact tracing and cluster isolation, and a detection paradox
论文作者
论文摘要
我们确定了与接触跟踪和群集隔离相关的一些随机变量的分布。这使我们能够将一般限制定理应用于超临界的碎屑 - 杂音分支过程。值得注意的是，我们明确计算所有分离的簇中给定大小的分离簇的渐近比例，条件是在流行病的存活下。令人惊讶的是，后者与典型簇的大小在检测时的分布有所不同。我们解释了这种悖论背后的原因。
We determine the distributions of some random variables related to a simple model of an epidemic with contact tracing and cluster isolation. This enables us to apply general limit theorems for super-critical Crump-Mode-Jagers branching processes. Notably, we compute explicitly the asymptotic proportion of isolated clusters with a given size amongst all isolated clusters, conditionally on survival of the epidemic. Somewhat surprisingly, the latter differs from the distribution of the size of a typical cluster at the time of its detection; and we explain the reasons behind this seeming paradox.
