Three types of studies have measured the relationship between schooling and COVID-19 infections. Two of them measure infections among students, teachers, or other staff who actually were present at a school during the pandemic. One of those two, emphasized in this paper, attempts to measure the source of infection as a contact made at school versus a contact made elsewhere in the community. The second type, also used in this paper, lacks information on infection source but compares prevalence to other groups of people who were not present at a school. Both of those study types can, with additional assumptions, help estimate the maximum infection students and staff might have avoided if they had instead been absent in school.
In practice, the two types of studies typically do not assess how the wider community is affected by the activities of students and staff. Wider community effects may have little relevance for the private costs and benefits of location decisions by students and staff, but they are relevant for estimating the social costs and benefits (Courtemanche et al., 2021). This third type of study is beyond the scope of this paper.
The frequency of in-school transmission
Additional data, discussed further below, are required to obtain estimates of the expected number of fatalities such as those shown in the final three columns of Table 1. Estimating the level of fatality risks from in-person schooling is the purpose of the remainder of the present paper. It requires estimates of the number of cases acquired in school and the number of cases acquired by remote learners during school hours, or at least estimates of the difference between the two. As a bounding exercise, I assume that zero cases are acquired by remote learners during school hours and then return to that assumption at the end of the paper.
Although this paper does not have access to original infection data, it does assemble published data from five distinct settings and puts their findings in common metrics. The metrics are selected for comparability with familiar risks and with metrics used in the literature on occupational safety and compensating differentials. Sometimes computation of the common metrics requires supplementing the published data with additional schooling data from the same setting of the published study.Footnote 10 In particular, the metrics account for the “duration of exposure” (U.S. Bureau of Labor Statistics, 2010), which for students and teachers is the amount of time they are present at school. The time dimension of risks, usually absent from epidemiology articles, is particularly relevant for private and public choices because the tradeoff between in-person and remote learning is a question of time allocation.
I found five published studies on school-acquired cases, one from Australia; England; North Carolina; Wood County, Wisconsin; and an Israeli school that experienced an outbreak.Footnote 11 The Australian study examines only the (rare) classrooms into which a student or staff entered with an infection during the study period, thus providing an “attack rate” rather than a rate of infection that accounts for the fact that on some days none of a person’s contacts at school would be infected. The similarities and differences between attack and infection rates are discussed further in the “Appendix” to this paper.
Ismail et al. (2020) looked at the entire country of England between June 1 and July 17, 2020, which is the summer half term as England “reopened after the first national lockdown”. For comparability with the other studies, I use their results for primary and secondary schools and supplement with attendance data from the UK Department for Education and prevalence data from Our World in Data. Most of the schools were open at some point during that time and the majority of staff appear to have been present. However, summer-term attendance was not mandatory and therefore student attendance overall was only about one-sixth of what it would be later in the fall and even less in secondary schools (Ismail et al., 2020; U.K. Office of Statistics Regulation, 2020). The types of students attending during the UK may be different from those attending during the fall term. Overall, 32 million staff days present and 43 million student days present in about 20,000 schools were covered by the study.
“Extensive social distancing and infection control measures were implemented with strict limitations on the number of staff and children in each bubble” (Ismail et al., 2020, p. 352). Ninety-six staff and eight student cases were identified by Public Health England (PHE) as potentially acquired in primary and secondary schools, although the study did not always verify that the person acquiring infection was ever in close contact with the primary case.Footnote 12 That is about 721,000 person-days per infection. Reweighting the student and staff infection rate to reflect the 15.4 teacher–pupil ratio that is normal during the academic year, that is 2.8 million person-days per infection. Taking an academic year as 180 days, that is 15,561 person-years per infection as shown in the first row of Table 2. New cases were low in England during that time; rescaling to the per capita new infections in the United States during its fall 2020 term yields about 707 person-years per school-acquired infection.Footnote 13
Note that all data in this subsection refer to COVID-19 infections rather than COVID-19 deaths, which are two orders of magnitude less common. The probabilities and rates being measured in Table 2 and following are very small and therefore not measured with high precision. The 15,561 person-years per infection (the inverse of a daily infection rate) can hardly be distinguished from 15,000, let alone from 15,562.
About half of the North Carolina’s school districts participated in some capacity in the study by Zimmerman et al. (2021). The participants were somewhat larger school districts with somewhat less in-person instruction than average. Many of the participating districts did not offer any in-person instruction and therefore did not provide any data for analysis herein. The authors explain how “districts were required to have universal masking for all ≥ 5 years of age (except the adapted curriculum, during meals, and when sufficiently distanced outside), implement 6-foot distancing, and wash hands … as well as perform daily symptom monitoring and temperature checks”, adding that “case adjudication of within-school transmission was performed via contact tracing by the local health department.” None of the schools offering in-person instruction had to terminate the instruction during the study period because of an outbreak or any other factor.
The study shows 90,338 in-person students and staff in the 11 districts providing in-school data over the 9 weeks of the study, which makes for a maximum of four million person-days. The study notes that somewhat more than 3000 persons quarantined at home at some point during the study, which I take to be 31,000 person-days out of the potential number.Footnote 14 Because many students were on hybrid schedules, I assume that half of the potential in-person days were spent off campus on scheduled remote learning, putting my estimate of in-person days at about 2.3 million, which is 12,732 person-years. With 32 cases acquired in school from August 15 through October 23, 2020, the inverse of the infection rate is about 398 person-years.Footnote 15 According to the COVID-testing data from the US Department of Health and Human Services (2021), the state of North Carolina’s positivity rate during its study was slightly less than the nationwide average rate for the full fall term. The final column of Table 2 therefore shows an inverse rate of about 377 when adjusted to US positivity rates.
The Wood County, Wisconsin study (Falk et al., 2021) involved about 5600 students and staff attending in person for at least part of the week. In-person elementary students attended every day. Middle and high school students attended half-days on average across the nine such schools in the study.Footnote 16 Mask wearing was required, students were organized in classroom cohorts of size 11–20, all classes and lunch periods were held indoors, and close contacts of positives were quarantined. I assume that quarantine days are the same percentage of the calendar as in North Carolina, except rescaled for the higher positivity rate in Wood County.
The study lasted 13 weeks (August 31–November 29), during which time typically seven holidays/teacher-workshops occurred, putting total time in person at about 1229 person-years. Seven cases were acquired in school during that time, putting the inverse infection rate at about 176 person-years. The average positivity rate in Wood County at that time exceeded even that of the highest US state rate (Montana) and was triple the US average. The final column therefore shows an adjusted inverse infection rate of about 549 person-years.
Table 2 reveals that surrounding-community COVID prevalence varies almost two orders of magnitude across studies. Although uniformly low by standards discussed further in the next section, the measured rates of school-acquired infection vary across the studies in close proportion to the surrounding-community prevalence, explaining why the final column of Table 2 varies much less than the second column. Ismail et al.’s (2020) study of England is large enough to investigate the proportionality hypothesis within their own study; they confirm that a region’s school-acquired infection rate is nearly proportional to its overall prevalence.
Estimating separate infection rates for students and staff is difficult because of the small numbers of transmissions in the North Carolina and Wisconsin studies. For what it is worth, the Wisconsin study found zero staff cases acquired in school. Of the 32 cases of in-school transmission found in the North Carolina study, none were student-to-staff. Most of the cases found in the English study were among staff, but the staff-pupil ratio was particularly high during the time of the study (summer break).
All of these studies raise concerns that cases are underestimated. However, under the weak assumption that true cumulative COVID-19 infections cannot exceed the population, cases generally are not undercounted by more than a factor of ten.Footnote 17 Furthermore, Sect. 5 below multiplies cases per capita by fatalities per case, which means that any proportional case measurement error that is common to the two sources will cancel for the purposes of assessing fatalities per capita.Footnote 18 The “Appendix”’s attack rate estimates also are interesting in that regard because the attack rate is a ratio of cases to cases. Even if Sect. 2’s fatality-rate estimates were multiplied by ten because of suspected undercounts, the rates would still be in the range of familiar risks.
None of the studies directly report person-days present in person, which is the denominator for my transmission rates. As described above, I have estimated based on information provided in the published articles together with supplemental information I found online. My point estimates of person-days per school-acquired infection (and thereby the estimates of person-years per school-acquired fatality that follow) can be understood as over- or underestimates in the same proportion that I over- or underestimated in-person attendance, respectively.
The North Carolina and Wisconsin studies measured community-acquired cases among their students and staff as well as school-acquired infections. Table 3 shows the corresponding (inverse) annualized infection rates for the student and teacher populations regardless of whether acquired in school or not. For that purpose, days outside of school are added to the person-years numerator from Table 2 and community-acquired cases added to the denominator; a year in Table 3 is 365 days rather than 180. The final column rescales the results to the US average positivity rate. The person years shown in Table 3 are about one-tenth those shown in Table 2 because (1) the North Carolina and Wisconsin studies found that the daily rate of acquiring a COVID-19 infection in school is, for students and staff, about one-twentieth of the rate of acquiring an infection from any source and (2) about half of calendar days are spent outside of school (weekends, and so on).Footnote 19
Relative prevalence among people present at school
Emily Oster (2020a, b) has led a “COVID-19 School Response Dashboard” project gathering attendance and prevalence data from participating schools in almost every US state. The prevalence measures are only for school students and staff, but do not distinguish infections acquired in school from those acquired at home or in the community. Table 3 therefore provides the appropriate comparison. Oster’s data show about 38 person-years per infection (i.e., an annual infection rate of about 1/38). The Wisconsin study finds a higher infection rate in a high-positivity area, which corresponds to a rescaled annual infection rate of about 1/46. The rescaled rate in the North Carolina study (Zimmerman et al., 2021) is about 1/37.
The Centers for Disease Control and Prevention (CDC) provides national case counts by age group, with the population-weighted sum across age groups yielding the national case counts. The CDC data can be reweighted to reflect the age of students, or the age of teachers, rather than the nation as a whole. The final rows of Table 3 show the results applied to the period September 1 through November 29, 2020.Footnote 20 The four sources shown in the table reveal similar infection rates once they are rescaled by the prevalence in the communities where the data were collected.
Bravata et al. (2021) look at prevalence gaps between US household types using a continuous measure of school visits derived from mobility data. They find a small positive relationship between school visits and cases in households with children, which they acknowledge is not entirely causal. They find a coefficient of essentially the same magnitude—but the opposite sign—for cases in households with teachers.
Sweden is an interesting comparison to the United States because it appears to be in between US COVID-19 and US seasonal flu on the scale of prevention effort in schools. For example, in Sweden during COVID-19 close contacts were not required to quarantine, class size did not have to be reduced, and face masks were not specifically recommended.Footnote 21 Vlachos et al. (2021) conclude that parents of an in-school child are 17% more likely, relative to parents of a remote learner, to have a positive polymerase chain reaction (PCR) test but 6% less likely to have a COVID diagnosis from a healthcare visit. Ludvigsson et al. (2021) find that teachers in Sweden had a relative risk of COVID-19 ICU admissions of 0.43 compared to a baseline of other non-healthcare occupations.
Arguably England, Wisconsin and North Carolina were “lucky” in that in-person school was not terminated during the study period owing to an outbreak. The present paper therefore additionally considers a hypothetical “high-risk” scenario in which Wood County (with its high community prevalence) experienced an outbreak, whose probability and intensity I measure from Israel as the number of infections in the Israeli school that had an outbreak divided by the nationwide number of student-days of in-person schooling that occurred between the opening of Israel’s schools to the reclosing upon outbreak (Stein-Zamir et al., 2020). That approach likely exaggerates the probability and intensity of an outbreak in US schools because (1) Israel was selected because it had an outbreak, (2) all but two of the cases in the Israeli school are assumed to come from the outbreak rather than the broader community, and (3) the outbreak school was not requiring masks and other mitigation methods commonly adopted in schools.Footnote 22
For comparison purposes, this paper also shows fatality risks in more familiar occupational and consumer contexts. The comparison of familiar risks with COVID-19 risks serves two purposes. One is to provide context given that a pandemic is a new experience for many people. Second, the comparisons show if the COVID-19 risks are in the range of risks that have been priced in labor and consumer markets (Viscusi, 1992; Viscusi & Aldy, 2003).
Table 4’s middle column shows fatality risks for selected pre-pandemic activities, sorted by fatality risk, from the National Census of Fatal Occupational Injuries published by the US Bureau of Labor Statistics (2020a, b). BLS measures the risks per year engaged in an occupation, not including fatalities experienced while commuting to work. The two riskiest occupations reported by BLS are “fishing and hunting workers” and loggers, which experience roughly 1000 person-years per fatality on the job. Farming has about 4000 person years per fatal injury on the job. Driving occupations—both truck drivers and sales workers—also average about 4000 person-years per fatality. Educational and health services industries, which include schools, were safer than the average (28,571 person-years per fatality) at 125,000 person-years per fatality.
On the consumer side, driving is a familiar fatality risk. Many adults, teachers included, commute to work daily by car. The US Department of Transportation (2017, 2020) measures automobile fatalities per mile traveled, which I convert to daily risks by selecting various commuting lengths.Footnote 23 The purpose here is not to estimate the modes or numbers of miles that teachers and students commute but rather to provide information on risks familiar to adults generally. Therefore, Table 2’s final column expresses the differences among occupations in terms of miles driven per day. For example, government workers normally experience less occupational risk than the average worker, but the combined occupational and commuting risk would be equal to the average if the government workers commuted 17 miles more per day than the average worker did.
Of particular interest is the final addendum row of the table. It combines pre-pandemic fatality risk for in-person teachers with the modal fall 2020 risk to self and spouse of death from school-acquired COVID-19, examined in more detail in the tables that follow. The combined risk for teachers (77,547 person-years per infection) is still less than even government workers generally experienced before the pandemic (55,556). The impact of COVID on the risk to the modal teacher and spouse is the equivalent of driving approximately four (= 26 − 22) additional miles each workday.
All such activities also involve prevention and treatment costs to reduce fatalities. Vehicles are built with seatbelts and engineering features to help protect passengers. Drivers and the legal system limit speeds, drunk driving and constrain other highway risks. Many auto injuries are not fatal because of medical resources spent to help the victim survive. Pandemic risks also have those qualitative features, including personal protective equipment and various hospitalization treatments. Unlike COVID-19, many familiar workplace accidents are neither infectious nor contagious, although automobile accidents often do involve third parties who are on foot or in another vehicle.
The distinction between accident and fatality is relevant for decision making, especially because the fatalities are comparatively rare. A new traffic pattern can, in principle, be monitored for accidents and modified before a fatality occurs.Footnote 24 With COVID-19, the infections are about 100 times more common than fatalities and the former can be monitored in a new schooling situation and adjusted before a fatality occurs.
Cases per fatality are expected to be greater in schools than all-adult workplaces because most of the people in school are children, who have low COVID mortality rates. In other words, schools would have a Bayesian advantage (from the perspective of preventing fatalities) over all-adult workplaces even if children were equally likely to transmit infections: cases among children serve as a warning to adults without posing the fatality risks of cases among adults. The Israeli outbreak was discovered in that way. Moreover, because being a student is a fairly homogeneous activity engaging tens of millions, schools can learn from each other faster than, say, a law office could learn from the accident results at a meatpacking factory. Although pandemics are not new, the learning rate is relevant because COVID-19 is far newer than automobiles or farm equipment.
Table 5 quantifies some of the Bayesian elements of fatality risks by analogizing motor-vehicle accidents to COVID infections, which is a way of reconciling infections (Tables 2, 3) with fatalities (Table 4). Motor vehicles have 345 reported accidents per motor vehicle fatality. COVID “accidents”—that is, cases—per fatality are of a similar order of magnitude. The general population experienced one COVID fatality per 56 cases. The school population had more cases per fatality—equivalently fewer fatalities per case—because it is younger than the general population. The lowest of the three case fatality rates, and therefore the most COVID accidents per fatality at 285, is in the school population limited to exclude the elderly. This final entry in Table 5 is potentially relevant for policymaking because, perhaps in an initial phase in which a school is uncertain as to whether its prevention protocols are sufficiently effective, students and teachers who live with elderly people could be excused from in-person attendance.