There is a pressing need for evidence-based scrutiny of plans to re-open childcare centres during the COVID-19 pandemic. Here we developed an agent-based model of SARS-CoV-2 transmission within a childcare centre and households. Scenarios varied the student-to-educator ratio (15:2, 8:2, 7:3), family clustering (siblings together versus random assignment) and time spent in class. We also evaluated a primary school setting (with student-educator ratios 30:1, 15:1 and 8:1), including cohorts that alternate weekly. In the childcare centre setting, grouping siblings significantly reduced outbreak size and student-days lost. We identify an intensification cascade specific to classroom outbreaks of respiratory viruses with presymptomatic infection. In both childcare and primary school settings, each doubling of class size from 8 to 15 to 30 more than doubled the outbreak size and student-days lost (increases by factors of 2–5, depending on the scenario. Proposals for childcare and primary school reopening could be enhanced for safety by switching to smaller class sizes and grouping siblings.

critical transition in dynamical systems 30,31. For instance, critical slowing down can precede both first-and second-order transitions 31,32 and is accompanied by the divergence of correlation length in a physical system 33. Many statistics have been used to study EWS in spatially extended systems; temporal 34,35 and spatial correlation 36,37 have been found to precede transitions in spreading processes. Other measurements have been applied to spin systems, where each site in a lattice may be in one of two possible states, possibly partially dependent on the state of neighbouring sites. The spin model has also been applied to opinion dynamics; a simple voter model with binary opinion dynamics is analogous to a physical spin system, where particles represent agents and spins represent different opinions 38. Consensus formation can be seen as a second-order phase transition to an ordered state (where all spins are aligned). In this regime, knowledge of the opinion of a single agent predicts the opinion of all other agents in the system 39. Since the transition in finite networks is smooth 40 , the distance across the network over which the opinions of connected agents are strongly correlated increases smoothly; this is analogous to divergence of the correlation length of a physical system 41. Above some critical temperature, disordered systems take the form of a spin glass. In a spatial opinion model, this describes a state where opinions between neighbours are generally uncorrelated 42. On a static network, this state induces a larger number of edges between dissimilar neighbours as compared to that of consensus regimes. This is related to join count statistics, where the numbers of edges between like neighbours are compared to the number between dislike neighbours as a test of geographical distribution. This is arguably the most natural and well-defined measure for graphs presenting binary data and is used for spatial analysis 43. The necessity of disease surveillance and early warning signals for outbreaks has been discussed in multiple contexts, from epidemic mitigation to bioterrorism prevention 44-46. Potential mitigation of unnecessary expense motivates us to find reliable EWS that remain easily computable on large high-resolution data sets. Furthermore, the study of EWS in coupled disease-behaviour multiplex networks has received relatively little attention, suggesting a significant gap in the literature. Our objective is to evaluate and compare the relative merits of the mutual information, Moran's I, Geary's C and join count statistics as EWS of the occurrence of epidemics and changes in aggregate opinion on a coupled disease-behaviour network model. We use three differently parametrised models (V1, V2 and V3) coupling a binary vaccination opinion dynamic to an SIRV epidemic process. The resulting trends in the EWS for model V2 will be explored in the Results and Discussion sections, with V1 and V3 presented in Supplementary Information S5. The outline of this paper is as follows: the Methods section wil...

The disruption of professional childcare has emerged as a substantial collateral consequence of the public health precautions related to COVID-19. Increasingly, it is becoming clear that childcare centers must be (at least partially) operational in order to further mitigate the socially debilitating challenges related to pandemic induced closures. However, proposals to safely reopen childcare while limiting COVID-19 outbreaks remain understudied, and there is a pressing need for evidence-based scrutiny of the plans that are being proposed. Thus, in order to support safe childcare reopening procedures, the present study employed an agent-based modeling approach to generate predictions surrounding risk of COVID-19 infection and student-days lost within a hypothetical childcare center hosting 50 children and educators. Based on existing proposals for childcare and school reopening in Ontario, Canada, six distinct room configurations were evaluated that varied in terms of child-to-educator ratio (15:2, 8:2, 7:3), and family clustering (siblings together vs. random assignment). The results for the 15:2 random assignment configuration are relevant to early childhood education in Ontario primary schools, which require two educators per classroom. High versus low transmission rates were also contrasted, keeping with the putative benefit of infection control measures within centers, yielding a total of 12 distinct scenarios. Simulations revealed that the 7:3 siblings together configuration demonstrated the lowest risk, whereas centres hosting classrooms with more children (15:2) experienced 3 to 5 times as many COVID-19 cases. Across scenarios, having less students per class and grouping siblings together almost always results in significantly lower peaks for number of active infected and infectious cases in the institution. Importantly, the total student-days lost to classroom closure were between 5 and 8 times higher in the 15:2 ratios than for 8:2 or 7:3. These results suggest that current proposals for childcare reopening could be enhanced for safety by considering lower ratios and sibling groupings.

Sudden shifts in population health and vaccination rates occur as the dynamics of some epidemiological models go through a critical point; literature shows that this is sometimes foreshadowed by early warning signals (EWS). We investigate different structural measures of a network as candidate EWS of infectious disease outbreaks and changes in popular vaccine sentiment. We construct a multiplex disease model coupling infectious disease spread and social contact dynamics. We find that the number and mean size of echo chambers predict transitions in the infection dynamics, as do opinion-based communities. Graph modularity also gives early warnings, though the clustering coefficient shows no significant pre-outbreak changes. Change point tests applied to the EWS show decreasing efficacy as social norms strengthen. Therefore, many measures of social network connectivity can predict approaching critical changes in vaccine uptake and aggregate health, thereby providing valuable tools for improving public health.

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