Division of Science, New York University Abu Dhabi, Abu Dhabi, 129188, UAE.
Università di Pavia, Pavia, Italy.
Sci Rep. 2022 Feb 22;12(1):3012. doi: 10.1038/s41598-022-06540-w.
Studies on the effects of school openings or closures during the Covid-19 pandemic seem to reach contrasting conclusions even in similar contexts. We aim at clarifying this controversy. A mathematical analysis of compartmental models with subpopulations has been conducted, starting from the SIR model, and progressively adding features modeling outbreaks or upsurge of variants, lockdowns, and vaccinations. We find that in all cases, the in-school transmission rates only affect the overall course of the pandemic above a certain context dependent threshold. We provide rigorous proofs and computations of the thresdhold through linearization. We then confirm our theoretical findings through simulations and the review of data-driven studies that exhibit an often unnoticed phase transition. Specific implications are: awareness about the threshold could inform choice of data collection, analysis and release, such as in-school transmission rates, and clarify the reason for divergent conclusions in similar studies; schools may remain open at any stage of the Covid-19 pandemic, including variants upsurge, given suitable containment rules; these rules would be extremely strict and hardly sustainable if only adults are vaccinated, making a compelling argument for vaccinating children whenever possible.
研究表明，即使在相似背景下，新冠大流行期间学校开放或关闭的影响似乎也得出了相互矛盾的结论。我们旨在澄清这一争议。我们从 SIR 模型出发，对具有亚群的房室模型进行了数学分析，并逐步添加了暴发或变异激增、封锁和疫苗接种等模型特征。我们发现，在所有情况下，校内传播率仅在一定背景相关阈值之上影响大流行的总体进程。我们通过线性化提供了阈值的严格证明和计算。然后，我们通过模拟和对数据驱动研究的回顾来验证我们的理论发现，这些研究显示出经常被忽视的相变。具体影响包括：对阈值的认识可以为数据收集、分析和发布提供信息，例如校内传播率，并澄清在相似研究中得出不同结论的原因；只要有适当的遏制规则，学校在新冠大流行的任何阶段都可以保持开放，包括变异激增；如果只有成年人接种疫苗，这些规则将非常严格且难以持续，这有力地证明了只要有可能就应给儿童接种疫苗。
