Figures and data in COVID-19 cluster size and transmission rates in schools from crowdsourced case reports

Version of Record

Accepted for publication after peer review and revision.

Download
Cite
Share
CommentOpen annotations (there are currently 0 annotations on this page).

Version of Record published: November 30, 2022 (This version)
Accepted Manuscript published: October 21, 2022 (Go to version)
Accepted: October 20, 2022
Preprint posted: December 8, 2021 (Go to version)
Received: December 7, 2021

Figures
Tables
Additional files

13 figures, 5 tables and 1 additional file

Figures

Figure 1

Download asset Open asset

Frequency of clusters of different sizes on a log scale.

Trends continue as shown for larger clusters. (Left) Fixing mean cluster size $R_{c} + 1$ and varying dispersion $k$ . (Right) Fixing $k$ and varying $R_{c} + 1$ .

Figure 2

Download asset Open asset

Histograms of observed cluster sizes in four Canadian provinces.

Inset histograms only show clusters of size 11 or more on a different scale.Each dot represents a single cluster of size 11 or larger, and indicates the presence of (more rare) larger clusters.

Figure 3

Download asset Open asset

Two indicators of COVID prevalence over time in the four Canadian provinces.

(Left) Estimates of the rate of new clusters (per 100,000 population) as a function of time in each province. (Right) Incident cases per day (per 100,000 population) in the same province over the corresponding time interval. Case counts are averaged over a 2-week window.

Figure 4

Download asset Open asset

Results of our analysis for the four Canadian provinces.

(Left) Estimates of mean and dispersion of cluster size for four Canadian provinces using the individual ascertainment model with ascertainment rate 0.75. Estimate of mean includes index case. The sample size for estimates for each province is the Number of Clusters as shown in Table 1. 95% confidence ellipses are shown, computed using the inverse Hessian method. (Right) Estimated distribution of $ν$ (left axis) and instantaneous transmission rate $β$ (right axis) for different provinces.

Figure 5

Download asset Open asset

For a range of mean cluster size and dispersion $k$ , the fraction of cases in the 20% largest clusters, counting only secondary cases (left), or all cases, index and secondary (right).

Dots indicate the location of the four provinces in the plots.

Figure 6

Download asset Open asset

Estimated distribution of $β$ for different provinces.

Figure 7

Download asset Open asset

Distribution of the number of secondary infections under baseline conditions and under three interventions.

Left: under parameter choice $R_{c} = 1$ and $k = 0.4$ . Right: with $R_{c} = 2.5$ .

Appendix 1—figure 1

Download asset Open asset

Histograms of observed cluster sizes in eight US states.

We only show clusters of size 30 or fewer. Each dot represents a single cluster of size 8 or larger, and indicates the presence of (more rare) larger clusters.

Appendix 1—figure 2

Download asset Open asset

Two indicators of COVID prevalence over time in the eight US states.

(Left) Estimates of the rate of new clusters being reported (per 100,000 population) as a function of time in each province. (Right) Incident cases per day (per 100,000 population) in the same province over the corresponding time interval. Case counts are averaged over a 2-week window.

Appendix 1—figure 3

Download asset Open asset

Estimates of mean and dispersion of cluster size for eight American states using the individual ascertainment model with ascertainment rate 0.75.

Estimate of mean includes index case. The sample size for estimates for each state is the Number of Clusters as shown in Appendix 1—table 1. 95% confidence ellipses are shown, computed using the inverse Hessian method.

Appendix 1—figure 4

Download asset Open asset

Estimates of mean and dispersion of cluster size for eight US states (left) and four Canadians provinces (right) using the individual ascertainment model (left) and the group ascertainment model (right) with varying ascertainment rate.

Estimates of mean includes index case.

Appendix 1—figure 5

Download asset Open asset

Estimates of mean and dispersion of cluster size for the four provinces with four different choices of the window for defining clusters.

Choices are 4, 7, and 10 days, with thicker lines on the error ellipse indicating more days.

The sample size for estimates for each province is the Number of Clusters as shown in Table 1 of the main text. 95% confidence ellipses are shown, computed using the inverse Hessian method.

Author response image 1

Download asset Open asset

Tables

Table 1

Cluster statistics for each province.

(Top) For each of the four Canadian provinces: number of clusters in the data, number of schools reported, number of schools with multiple clusters, fraction of schools with multiple clusters. (Bottom) Fraction of clusters with one case, mean observed cluster size, maximum observed cluster size, and index of dispersion (variance of number of cases divided by mean number of cases) with and without subtracting one for the index case.

Province	Number of Clusters	Number of Schools	Schools with Multiple clusters	Fraction of schools Multiple clusters
Manitoba	1754	542	396	0.73
Saskatchewan	1211	466	295	0.63
Ontario	8482	3337	2147	0.64
Alberta	5032	1537	1158	0.75
Province	Fraction with	Mean observed	Max observed	Index of	IoD without
Province	One case	Cluster size	Cluster size	Dispersion (IoD)	Index case
Manitoba	0.58	2.16	44	3.44	6.43
Saskatchewan	0.66	1.70	16	1.23	2.98
Ontario	0.63	1.83	50	1.87	4.13
Alberta	0.47	2.45	108	4.94	8.35

Table 2

Properties of the estimated distribution for the Poisson parameter $ν$ , the index case-specific expected number of further cases in a cluster.

The expected value of $ν$ is $R_{c}$ and its distribution gives important information about overdispersion of clusters. In units of hours^-1.

Province	Mean	Standard deviation	Median	90th percentile	99th percentile
Alberta	1.86	2.55	8.9e-01	5.0	11.9
Manitoba	1.43	2.45	4.3e-01	4.1	11.7
Saskatchewan	0.88	1.46	2.9e-01	2.5	7.0
Ontario	1.04	1.70	3.5e-01	3.0	8.1

Table 3

Properties of the estimated distribution for the instantaneous transmission rate β.

In units of hours^-1.

Jurisdiction	Mean	Standard deviation	Median	90th percentile	99th percentile
Alberta	4.8e-03	6.7e-03	2.2e-03	1.3e-02	3.2e-02
Manitoba	3.3e-03	5.5e-03	1.1e-03	9.5e-03	2.6e-02
Saskatchewan	2.5e-03	4.4e-03	7.4e-04	7.4e-03	2.1e-02
Ontario	2.5e-03	4.1e-03	7.8e-04	7.1e-03	2.0e-02

Appendix 1—table 1

Cluster statistics for each state in the US data.

(Top) For each of the eight US states: number of clusters in the data, number of schools reported, number of schools with multiple clusters, fraction of schools with multiple clusters. (Bottom) Fraction of clusters with one case, mean observed cluster size, maximum observed cluster size, and index of dispersion (variance of number of cases divided by mean number of cases) with and without subtracting one for the index case.

State	Number of Clusters	Number of Schools	Schools with Multiple clusters	Fraction of Multiple schools clusters
Texas	369	326	30	0.09
Florida	147	134	10	0.07
Ohio	122	95	12	0.13
Pennsylvania	322	247	46	0.19
Wisconsin	130	118	11	0.09
Georgia	68	53	10	0.19
Indiana	105	84	13	0.15
Illinois	81	76	5	0.07
State	Fraction with One case	Mean observed Cluster size	Max observed Cluster size	Index of Dispersion (IoD)	IoD without Index case
Texas	0.69	1.73	21	2.29	5.40
Florida	0.69	5.31	90	27.28	33.62
Ohio	0.69	2.11	21	4.30	8.18
Pennsylvania	0.73	1.75	28	3.84	8.95
Wisconsin	0.46	4.02	31	6.28	8.36
Georgia	0.46	4.76	38	10.09	12.77
Indiana	0.81	2.19	36	9.00	16.56
Illinois	0.52	3.47	36	11.07	15.55

Appendix 1—table 2

Estimates of dispersion $k$ and mean cluster size $R_{c} + 1$ for the four provinces for three choices of the cluster definition window: 4 days, 7 days (the choice in the main text), and 10 days.

Province	Dispersion $k$			Mean cluster size $R_{c} + 1$
Province	4 days	7 days	10 days	4 days	7 days	10 days
Manitoba	0.36	0.34	0.35	1.99	2.43	2.71
Saskatchewan	0.34	0.37	0.36	1.76	1.88	1.98
Ontario	0.36	0.37	0.40	1.74	2.04	2.24
Alberta	0.50	0.53	0.54	2.43	2.86	3.16

Additional files

Transparent reporting form: https://cdn.elifesciences.org/articles/76174/elife-76174-transrepform1-v2.pdf
Download elife-76174-transrepform1-v2.pdf

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Article PDF

Open citations (links to open the citations from this article in various online reference manager services)

Mendeley

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

Paul Tupper
Shraddha Pai
COVID Schools Canada
Caroline Colijn

(2022)

COVID-19 cluster size and transmission rates in schools from crowdsourced case reports

eLife 11:e76174.

https://doi.org/10.7554/eLife.76174

Share this article

Cite this article

Frequency of clusters of different sizes on a log scale.

Histograms of observed cluster sizes in four Canadian provinces.

Two indicators of COVID prevalence over time in the four Canadian provinces.

Results of our analysis for the four Canadian provinces.

For a range of mean cluster size and dispersion k, the fraction of cases in the 20% largest clusters, counting only secondary cases (left), or all cases, index and secondary (right).

Estimated distribution of β for different provinces.

Distribution of the number of secondary infections under baseline conditions and under three interventions.

Histograms of observed cluster sizes in eight US states.

Two indicators of COVID prevalence over time in the eight US states.

Estimates of mean and dispersion of cluster size for eight American states using the individual ascertainment model with ascertainment rate 0.75.

Estimates of mean and dispersion of cluster size for eight US states (left) and four Canadians provinces (right) using the individual ascertainment model (left) and the group ascertainment model (right) with varying ascertainment rate.

Estimates of mean and dispersion of cluster size for the four provinces with four different choices of the window for defining clusters.

Cluster statistics for each province.

Properties of the estimated distribution for the Poisson parameter ν, the index case-specific expected number of further cases in a cluster.

Properties of the estimated distribution for the instantaneous transmission rate β.

Cluster statistics for each state in the US data.

Estimates of dispersion k and mean cluster size Rc+1 for the four provinces for three choices of the cluster definition window: 4 days, 7 days (the choice in the main text), and 10 days.

Transparent reporting form

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

For a range of mean cluster size and dispersion $k$ , the fraction of cases in the 20% largest clusters, counting only secondary cases (left), or all cases, index and secondary (right).

Estimated distribution of $β$ for different provinces.

Properties of the estimated distribution for the Poisson parameter $ν$ , the index case-specific expected number of further cases in a cluster.

Estimates of dispersion $k$ and mean cluster size $R_{c} + 1$ for the four provinces for three choices of the cluster definition window: 4 days, 7 days (the choice in the main text), and 10 days.