A new threshold reveals the uncertainty about the effect of school opening on diffusion of Covid-19

Abstract

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.

Designing school reopening in the COVID-19 pre-vaccination period in Bogotá, Colombia: A modeling study

“…The evaluation of the impact on COVID-19 dynamics caused by school reopening depends on the epidemiological context. Hence, the predicted effectiveness of interventions to reduce transmission will often depend on whether the intervention reduces the reproduction number below 1, which can be sensitive to the model's parameters [37]. This effect means that, for example, the level at which school reopening capacity is optimized can be difficult to precisely quantify.…”