AI 中文总结
该研究针对定向多层流，发现聚合流动性会掩盖流行病入侵路径，给出恢复路径构成的充要条件，经流感、新冠疫情案例验证，分层流动性分析比聚合更具监测价值。
AI 中文摘要
流行病模型常将航空出行、通勤及其他流动性层聚合为单一加权网络。聚合虽保留了流入某区域的总输入感染数，但丢失了传递感染的交通方式与路径，而这是特定交通方式干预所需的关键信息。我们针对具有重尾变异的定向多层流明确了这一点：聚合是一种非对称滤波器，极端输入的幅度（其径向尾指数）是采样与非负聚合的精确不变量，而其在各层与路径间的构成（角度部分）会被特定层的采样重新加权，且可能被不可逆合并。我们给出了恢复路径构成的充要条件，为该损失附加了监测决策成本，并证明首次确立的路径未必是最繁忙的。一项受控的种群间研究对该成本进行了校准，两项对比重建展示了其影响场景：在美国流感大流行中，航空出行提供了通勤之外的拟合信息，分层排名比聚合排名能定位更多航空输入负担；在意大利早期新冠疫情波中，通勤改善了发病重建，而航空归因仍未解决。因此，聚合可支持总输入感染监测，但通常无法识别输入背后的交通方式或路径。
英文摘要
Epidemic models often pool air travel, commuting, and other mobility layers into a single weighted network. Pooling keeps the total imported infections into a region but discards the transport mode and route that delivered them, the information a mode-specific intervention needs. We make this precise for directed multilayer flows with heavy-tailed variation. Pooling acts as an asymmetric filter. The magnitude of an extreme importation, its radial tail index, is an exact invariant of sampling and nonnegative aggregation, whereas its composition across layers and routes, the angular part, is reweighted by layer-specific sampling and can be irrecoverably merged. We give a necessary and sufficient condition for recovering route composition, attach a surveillance decision cost to the loss, and show that the first established route need not be the busiest. A controlled metapopulation study calibrates the cost, and two contrasting reconstructions show where it bites. In US pandemic influenza, air adds fitted information beyond commuting, and a layer-resolved ranking targets more air-import burden than a pooled one. In the early Italian COVID-19 wave, commuting improves onset reconstruction while air attribution stays unresolved. Pooling can therefore support total-importation surveillance but cannot in general identify the mode or route behind an importation.
