Memorial University of Newfoundland and Labrador, Canadian Network for Modelling Infectious Disease, Mathematics for Public Health, One Health Modelling Network for Emerging Infections


In Fall 2021, Canadian children under 12 years old will return to school unvaccinated. These unvaccinated children are more susceptible to COVID-19 infection, and will attend elementary schools with other unvaccinated children where they are more likely to be exposed. Given these factors, we ask are elementary schools more at risk of large COVID-19 outbreaks? And if so, should we manage COVID-19 differently in elementary schools relative to high schools or other similar workplaces?

Infection spread in schools

Despite students being unvaccinated, elementary schools are less at risk of large COVID-19 outbreaks because elementary school students remain with the same classmates throughout the day, while high school students have different classmates in different classes. Tupper et al. 2020 considered the average number of infections due to an infected student attending either elementary or high school for 5 days (the “event reproduction number”) and found that 47 new infections would arise in high schools, and 21.8 in elementary schools, from one infected student attending school for 5 days when students do not wear masks. Tupper and colleagues’ assumed the original variant of COVID-19, and when we extend their analysis to consider the delta variant and improved ventilation in classrooms, we estimate 40 new infections in high schools, and 17 new infections in elementary schools, from one infected student attending school for 5 days when students do not wear masks (Table 1).

These calculations assume that high school students are in close contact with 8 different groups of 10 students for 3 hours during a 24 hour school week, and elementary school students are in close contact with 25 students for a 30 hour school week. In the high school, 40 new infections represents 51% of the cohort, and in the elementary school, 17 new infections is 69% of the cohort. In either school setting, even with masks being worn, one infected student can generate many new infections (Table 1), such that measures to prevent an infected child from attending school, for example testing programs or pausing activities to complete contact tracing, are warranted when all other classmates are unvaccinated.

But, how do these conclusions change with vaccination?

Vaccination

When 75% of high school students are vaccinated, the average number of new infections generated by one infected student is similar to that of an elementary school with all students unvaccinated: 7 or 10 symptomatic infections in the high school, and 10 or 13 symptomatic infections in the elementary school, arising from 5 days of school attendance and depending on whether students wear masks (Table 1). Due to vaccination and a larger cohort, infections are a much lower percentage in high schools: 19% or 27% experience a symptomatic or asymptomatic infection in the high school, as compared to 54% or 69% in the unvaccinated elementary school, depending on if masks are worn.

In the high school, substantial gains are possible by increasing vaccination to 95%. Then, after 5 days of school attendance an infected student generates, on average, just 3 or 5 new symptomatic infections depending on if masks are worn (Table 1). This represents a more slowly growing outbreak that will be easier to manage. In the high school, if only one measure can be implemented, increasing vaccination from 75% to 95% is more impactful than wearing masks (Table 1).

We assumed that vaccines prevent symptomatic infections and that 4% of symptomatic infections are hospitalized (see BC COVID-19 Modelling Group Report, August 18, 2021). As such, an outbreak of 25 or more symptomatic infections is expected, on average, to result in a hospitalization.

In addition to the mean number of new infections generated by one infected student attending school for 5 days, we calculated the distribution of new infections to show that, due to random chance, the number of new infections may be much larger or smaller than the mean (Figure 1).

Table 1. The mean number of cases for elementary and high schools when an infected student attends school for 5 days. all counts both asymptomatic and symptomatic infections, and percent expresses all relative to the size of the cohort (elementary schools - 25, high schools - 80). Parameter values are based on Tupper et al. 2020 (see Assumptions for full details).

##       school mask vaccinated symptomatic hospitalization  all percent
##  High school  yes         95         3.1             0.1 11.5    14.4
##  High school   no         95         4.6             0.2 16.6    20.7
##  High school  yes         75         6.9             0.3 15.3    19.1
##  High school   no         75         9.8             0.5 21.5    26.9
##   Elementary  yes          0         9.9             0.5 13.5    53.8
##   Elementary   no          0        13.2             0.7 17.2    68.7
##  High school  yes          0        21.0             0.9 30.0    37.5
##  High school   no          0        29.3             1.4 40.3    50.4

Figure 1. The distribution of the number of new infections arising from one infected student attending school for 5 days. Table 1 reports the mean, but due to random occurrences a range of new infections arising from one infected individual are possible with various probabilities.

Conclusion

If infection is introduced to an unvaccinated elementary school classroom, a large fraction of the students will be infected. Therefore, early detection through testing (of all members of the community, but particularly children under 12), and isolation of infected elementary school children is necessary to prevent the introduction of infection to elementary schools, and prevent a substantial outbreak. Requiring masks will slow infection spread, but outbreaks will still be substantial, so early containment is necessary. For high schools with 75% of students vaccinated, recommendations are similar and increasing vaccination to 95% will result in a slow-growing outbreak that is substantially easier to manage.

Assumptions

The event reproduction number is the average number of new infections due to one infected person attending an event, such as school (Tupper et al. 2020). To account for vaccination, we redefine \(k\) (Tupper et al. 2020) as a random variable following a binomial distribution, and as the number of individuals who interact with an infected person and are unvaccinated, or are vaccinated and experience a breakthrough infection. The event reproduction number assumes that an infected person attends an event, and we note that infections may be more readily introduced into an elementary school because students are unvaccinated and more likely to be infected at home or in the community. The event reproduction number does not consider infections that spread from those infected by the individual who introduced the infection to the school. The event reproduction number measures the value of one infected student isolating at home, and not the number of cases in the school after 5 days.

Vaccine efficacy against infection (symptomatic or asymptomatic) is assumed to be 70%, and we note that estimates of this value range between 55 and 80% (Richterman et al. 2021). For consistency with the BC COVID-19 Modelling Group Report, August 18, 2021) we assume 94% vaccine efficacy against symptomatic infection, and that 4% of symptomatic infections are hospitalized (including the Intensive Care Unit, and for both vaccinated and unvaccinated individuals).

Epidemiological parameters are as suggested in Tupper et al. 2020 (Elementary schools: \(k=25\) students, \(T=30\) hours, \(\tau = 30\) hours, \(\beta_{0} = 0.05\) per hour; High schools: \(k=10\) students, \(T=24\) hours, \(\tau=3\) hours, \(\beta_{0} = 0.3\) per hour, where \(\beta_0\) denotes the transmission rate for the original variant). We assumed the reproduction number for the delta variant is 50% greater (Scientific Pandemic Influenza Group on Modelling, June 2, 2021) than the alpha variant, which is 50% greater than the original variant (Davies et al. 2021). Our calculations assumed \(\beta_{\delta} = \beta_0(1+0.5/T)^2\) per hour. We estimated \(\beta\) by multiplying \(\beta_\delta\) by vaccine efficacies and the probabilities associated with different infection types: all cases, symptomatic, and hospitalizations. We assumed 35% of cases are asymptomatic (Sah et al. 2021). Tupper et al. 2020 assumed that masking and improved ventilation reduce the transmission rate, \(\beta\), by 50% and we use this value to consider the effects of masks. We assumed that the effects of masks and ventilation are equal and additive, and our ‘no mask’ scenarios assume that steps have been taken to improve ventilation.