Model-Estimated Association Between Simulated US Elementary School–Related SARS-CoV-2 Transmission, Mitigation Interventions, and Vaccine Coverage Across Local Incidence Levels

Key Points

Question  How is COVID-19 incidence in elementary school communities associated with in-school mitigation (eg, masks), vaccination, and local incidence, and when should decision-makers add or remove mitigation measures?

Findings  In this decision analytic model with a simulated population of 638 students and 60 educators and staff in an elementary school, school community incidence decreased with mitigation and vaccination and increased with local incidence. Thresholds for changing mitigation measures depended on the objective (eg, minimizing likelihood of any in-school transmission vs maintaining cases within acceptable limits).

Meaning  These findings suggest that appropriate increases and decreases for in-school mitigation depend on policy makers’ goals; responsive plans, in which mitigation is deployed based on local COVID-19 incidence and vaccine uptake, may be appropriate.

Importance  With recent surges in COVID-19 incidence and vaccine authorization for children aged 5 to 11 years, elementary schools face decisions about requirements for masking and other mitigation measures. These decisions require explicit determination of community objectives (eg, acceptable risk level for in-school SARS-CoV-2 transmission) and quantitative estimates of the consequences of changing mitigation measures.

Objective  To estimate the association between adding or removing in-school mitigation measures (eg, masks) and COVID-19 outcomes within an elementary school community at varying student vaccination and local incidence rates.

Design, Setting, and Participants  This decision analytic model used an agent-based model to simulate SARS-CoV-2 transmission within a school community, with a simulated population of students, teachers and staff, and their household members (ie, immediate school community). Transmission was evaluated for a range of observed local COVID-19 incidence (0-50 cases per 100 000 residents per day, assuming 33% of all infections detected). The population used in the model reflected the mean size of a US elementary school, including 638 students and 60 educators and staff members in 6 grades with 5 classes per grade.

Exposures  Variant infectiousness (representing wild-type virus, Alpha variant, and Delta variant), mitigation effectiveness (0%-100% reduction in the in-school secondary attack rate, representing increasingly intensive combinations of mitigations including masking and ventilation), and student vaccination levels were varied.

Main Outcomes and Measures  The main outcomes were (1) probability of at least 1 in-school transmission per month and (2) mean increase in total infections per month among the immediate school community associated with a reduction in mitigation; multiple decision thresholds were estimated for objectives associated with each outcome. Sensitivity analyses on adult vaccination uptake, vaccination effectiveness, and testing approaches (for selected scenarios) were conducted.

Results  With student vaccination coverage of 70% or less and moderate assumptions about mitigation effectiveness (eg, masking), mitigation could only be reduced when local case incidence was 14 or fewer cases per 100 000 residents per day to keep the mean additional cases associated with reducing mitigation to 5 or fewer cases per month. To keep the probability of any in-school transmission to less than 50% per month, the local case incidence would have to be 4 or fewer cases per 100 000 residents per day.

Conclusions and Relevance  In this study, in-school mitigation measures (eg, masks) and student vaccinations were associated with substantial reductions in transmissions and infections, but the level of reduction varied across local incidence. These findings underscore the potential role for responsive plans that deploy mitigation strategies based on local COVID-19 incidence, vaccine uptake, and explicit consideration of community objectives.

To balance the educational and social and emotional benefits of in-person education with concerns about SARS-CoV-2 transmission in school settings, the US Centers for Disease Control and Prevention (CDC) recommends using a layered mitigation approach in kindergarten to 12th grade (K-12) schools. Some components of this approach include vaccination for all eligible students and educators and staff, improved ventilation, and indoor masking regardless of vaccination status.¹ Individual states and school districts make local decisions about whether and how to incorporate these recommendations, and requirements for indoor masking have particularly generated debate.² In communities with high vaccination rates and low COVID-19 incidence, or where masking is less widely accepted, many schools are considering removing masks and other elements of mitigation.^3,4

While multiple studies indicate that masks are effective at mitigating the transmission of upper respiratory viruses,^5-10 they are generally viewed as a temporary measure.^11,12 Masks are physiologically safe, but there are limited data on the impact of mask-wearing on learning and social and emotional development, especially for younger children, students with special learning needs, and English language learners.^9,13 With the availability of vaccines for all US residents aged 5 years and older, many public health experts have called for “off-ramps” and “on-ramps” that use available public health data to inform decisions about when to remove or reinstate masking and other mitigation measures.^11,12,14,15

Establishing these off-ramps and on-ramps requires decision-makers to be explicit about the objectives they seek to achieve, which in turn necessitates a quantitative estimate of the epidemiologic consequences of adding or removing mitigation. We used a previously published simulation model of SARS-CoV-2 transmission within an elementary school community to generate estimates across a range of potential assumptions about intervention effectiveness, student vaccine coverage, and observed local COVID-19 incidence.¹⁶ We evaluated decision thresholds for multiple objectives to support decision-makers across different contexts.

We simulated an elementary school with 638 students in 30 separate classes and 60 educators and staff. Household members included 2 adults in each student household (with sibling students grouped in the same household) and 1 additional adult in each educator and staff household. The study adheres to the Consolidated Health Economic Evaluation Reporting Standards (CHEERS) reporting guidelines¹⁷ and was designated not human participant research by the Mass General Brigham institutional review board.

The model simulates infection dynamics within the immediate school community (students, educators and staff, and family members) and tracks infections over 30 days. At school, students, educators, and staff interact: within classrooms, during so-called specials classes (eg, related arts), and through random contacts. Outside of school, students and educator and staff interact with household members and other families (simulating social interactions or shared childcare). SARS-CoV-2 is introduced to the immediate school community at a rate proportional to the observed incidence rate for the wider local community (after accounting for an assumed case ascertainment rate).

Transmissions from infected people are modeled as a function of the age (student vs adult) of the infected individual and contact, vaccination status of the contact, and duration and location of exposure, with the latent and infectious periods drawn from distributions with means of 3.5 and 5 days, respectively.^18-23 In-school mitigation measures are simulated as a relative risk reduction on in-school transmission risk. Symptomatic students, educators, and staff with a clinical (vs subclinical) infection are offered diagnostic testing; for selected scenarios, we included weekly polymerase chain reaction screening offered to all students, educators, and staff. People identified with SARS-CoV-2 isolate for 7 days, and in-school contacts quarantine for 7 days. (We assumed all members of a classroom are in-school contacts). Additional details on the model structure are in eMethods 1 in the Supplement and the article by Bilinski et al.¹⁶

Selected input parameters are listed in the Table, eMethods 1 and eMethods 2 in the Supplement.^16,18-50 Bilinski et al¹⁶ describe other model input.

We assumed full-day symptomatic adult-to-adult in-school “secondary attack rates” (SARs) of 2%, 3.5%, and 7% per day for the wild-type virus, Alpha variant, and Delta variant, respectively (eMethods 1 in the Supplement). The full-day SAR is defined as the proportion of susceptible adults exposed to a symptomatic adult index case who acquire SARS-CoV-2 infection per day of contact in the absence of mitigation. Wild-type and Alpha variants are included to provide results against which schools can compare observed data from the 2020 to 2021 academic year. We assumed that elementary students were half as infectious as adults in schools and equally infectious in household settings.^16,32

Using infection fatality rate and in-hospital mortality rates provided by the CDC for use in COVID-19 models and relative hospitalization rates in different age groups, we assumed hospitalization risks among unvaccinated students and adults (aged 18 to 49 years) with COVID-19 of 0.1% and 2.4%, respectively, and a negligible risk among vaccinated individuals younger than 49 years (eMethods 1 in the Supplement).^42-44

In the base case, we assumed 70% uptake of 2-dose vaccination among adults (including educators, staff, and household members), reflecting US national data,⁴⁵ along with 4 potential scenarios of student vaccine uptake (0%, 25%, 50%, and 70%). In sensitivity analyses, we examine 50% adult vaccine uptake and a scenario in which both adults and students have 90% uptake. Given recent observational data on waning vaccine effectiveness, we assumed a base case of 70% vaccine effectiveness,^46-50 along with sensitivity analyses at 90%, 50%, and 25% effectiveness (eMethods 1 in the Supplement).

In the absence of data on the independent impact of individual mitigation measures on transmission, we estimated wide ranges for the effectiveness of 3 packages of interventions: simple ventilation and handwashing (group A; 20%-40% effective); group A plus universal masking (group B; 60%-80% effective); and full implementation of CDC-recommended measures¹ from 2020 to 2021 (eg, group B plus physical distancing of 3-6 feet when masked and >6 when unmasked, daily cleaning of surfaces, restrictions on shared items, and cohorting of students) (group C; 90%-100% effective). Group A effectiveness was based on the results of available airflow and air quality studies^51,52; group B effectiveness was based on both clinical as well as droplet and/or aerosol studies evaluating masking effectiveness^5-10 and a study evaluating the combination of masking and ventilation in a controlled environment⁵³; and group C effectiveness was based on observed risk of in-school transmission (0%-3% over the full infectious period) in schools implementing a full suite of mitigation measures in 2020 to 2021 (eMethods 2 in the Supplement).^54-56 The estimates for A and B are based on limited available data and remain highly uncertain; approximate ranges are used to understand the potential consequences of moving between mitigation approaches, and schools may define their specific values within each range based on local degree of implementation.

The base case included scenarios reflecting wild-type virus, Alpha variant, and Delta variant, different student vaccination coverage (0%, 25%, 50%, and 70% coverage), and 70% adult vaccination uptake. For each variant, we ran the model across a range of observed local incidence levels (0-50 cases per 100 000 residents per day, assumed 33% of cases observed) and in-school mitigation effectiveness (0%-100% reduction to in-school attack rate). To present smoothed results across these continuous ranges and manage the relatively high degree of model stochasticity from discrete model output, we constructed a regression-based meta-model from the raw model output to estimate the outcomes of interest (eMethods 3 in the Supplement).⁵⁷ We conducted the sensitivity analyses discussed previously only on the Delta variant scenarios, as these are most relevant for current decision-making.

We evaluated 2 primary outcomes over a 30-day period: (1) probability of any in-school SARS-CoV-2 transmission at each level of mitigation effectiveness and (2) mean increase in total infections among students, educators, staff, and their household members (ie, the immediate school community) associated with moving from more to less intensive mitigation measures (eg, unmasking). For the second outcome, we projected the increase in cases associated with each of 3 discrete changes in mitigation effectiveness, reflecting possible values of the difference between the A and B mitigation scenarios described previously, ie, a change from 60% to 40% mitigation effectiveness (between inner bounds of the respective effectiveness estimates); from 70% to 30% effectiveness (between midpoints); and from 80% to 20% effectiveness (between outer bounds). We identified the observed local incidence thresholds at which policy makers might add or remove mitigation interventions for objectives tied to these outcomes: (1) keeping the monthly probability of in-school transmission less than 25%, 50%, or 75% or (2) keeping the number of cases added to the immediate school community by removing mitigation fewer than 3, 5, or 10 cases per month.

In addition to these primary outcomes, we also evaluated the approximate number of additional hospitalizations that would result from shifting from more to less intensive mitigation by applying the approximate hospitalization risks in the Table to the second primary outcome. We then calculated local incidence thresholds for the objectives of keeping additional hospitalizations less than 1, 3, or 5 hospitalizations per 100 000 individuals in the immediate school community per month.

The model and all analyses were implemented in R version 4.0.2 (R Project for Statistical Computing),⁵⁸ and the replication code is publicly available.⁵⁹ Rather than conducting traditional statistical tests, which are not appropriate for this type of model-based analysis, we assessed the variability in the outcomes using the sensitivity analyses described previously.

Over 30 days in the simulated elementary school, all outcomes (probability of at least 1 in-school SARS-CoV-2 transmission and the additional cases and hospitalizations associated with decreased mitigation) were substantially higher with the Delta variant and with increased local incidence and lower with increased mitigation effectiveness and higher student vaccination uptake (Figure 1 and Figure 2; eFigure 1 in the Supplement). The local incidence decision thresholds associated with meeting different objectives based on these outcomes (eg, keeping risk of in-school transmission <50%) varied across the different scenarios (Figure 3).

With the Delta variant and 0% student vaccination, if removing masks (or other mitigation measures) was associated with a decrease in mitigation effectiveness to 30% (mitigation group A midpoint), decision-makers who seek to keep the monthly probability of in-school transmission less than 50% could remove masks at or below an observed local incidence of approximately 2 cases per 100 000 residents per day (Figure 1A). With student vaccination rates of 25%, 50%, or 70%, this threshold changed minimally to 3 to 4 cases per 100 000 residents per day (Figure 1A). Thresholds for keeping transmission probability less than 25% and less than 75% are presented in Figure 3 (for the Delta scenario) and in the Supplement for Alpha and wild-type scenarios (eTable 1 and eTable 2 in the Supplement).

With the Delta variant and 0% student vaccination, if unmasking (or removing other mitigation measures) is associated with a decrease in mitigation effectiveness from 70% (group B midpoint) to 30% (group A midpoint), decision-makers who seek to keep the number of additional infections associated with removing mitigation (eg, masks) fewer than 5 per month in the immediate school community could remove masks at or below a local incidence of approximately 5 cases per 100 000 residents per day (Figure 2A). With student vaccination rates of 25%, 50%, or 70%, this threshold changed to 7, 10, or 14 cases per 100 000 residents per day, respectively (Figure 2A). If the consequences of removing masks were smaller (eg, a 60% to 40% decreases in effectiveness), these thresholds would be higher (10-32 cases per 100 000 residents per day) (Figure 2). Thresholds for keeping additional cases less than 3 or 10 infections per month are presented in Figure 3 (for the Delta scenario) and in the Supplement for the Alpha and wild-type scenarios (eTable 1 and eTable 2 in the Supplement).

The rate of additional hospitalizations associated with decreases in mitigation effectiveness mirrored the additional cases and had a similar association with local incidence and student vaccination coverage (eFigure 1 in the Supplement). The local incidence thresholds required to keep the number of additional hospitalizations from mitigation reductions less than 1 per 100 000 individuals in the immediate school community per month were 21 or fewer cases per 100 000 residents per day across a range of student vaccination and mitigation effectiveness values, except with 90% vaccination for both students and adults (Figure 3). The thresholds were higher for an objective of keeping additional hospitalizations fewer than 5 per 100 000 individuals in the immediate school community per month, although still 29 or fewer cases per 100 000 residents per day for the larger changes in mitigation effectiveness (eg, 70% to 30%) with a student vaccination rate of 25% or less.

When adding weekly screening of students, educators, and staff in the Delta variant scenarios, the additional cases associated with changes in mitigation effectiveness decreased substantially (Figure 4A). Assuming a decrease in mitigation effectiveness from 70% to 30%, a 50% student vaccination rate, and a goal of fewer than 5 additional cases per month in the immediate school community, decision-makers could remove mitigation at or below a local incidence of approximately 21 cases per 100 000 residents per day when weekly screening is implemented, compared with 10 cases per 100 000 residents per day with only diagnostic testing (Figure 4A, eTable 4 in the Supplement). Similarly, the probability of at least 1 in-school transmission per month decreases with the implementation of weekly screening, although the changes in decision thresholds are less stark (eFigure 3 and eTable 4 in the Supplement). The 50% and 25% vaccine effectiveness analyses (Figure 4B; eFigure 4, eFigure 5, eTable 5, and eTable 6 in the Supplement) showed increased transmission and smaller changes in the decision thresholds across student vaccination coverage compared with the 70% and 90% effectiveness analyses (Figure 1, Figure 2, Figure 3, and Figure 4; eFigure 6 and eTable 7 in the Supplement). Higher vaccination coverage in both adults and students substantially increased the local incidence thresholds (Figure 3), while lower adult vaccine coverage (ie, 50%) only moderately changed model-estimated decision thresholds, aside from the additional hospitalization objectives. The hospitalization results were sensitive to the adult vaccination rate given that unvaccinated hospitalization risk is highest in adults and we assumed complete vaccine protection against hospitalization (a conservative assumption regarding the consequences of unmasking) (eFigure 2 and eTable 3 in the Supplement).

We used a previously published agent-based dynamic transmission model to examine the association between vaccine uptake and effectiveness, in-school mitigation measures including masking, observed local COVID-19 incidence, and SARS-CoV-2 transmissions in an elementary school community. In order to inform ongoing decisions about masking and other measures in schools, we identified thresholds of observed local COVID-19 incidence at which decision-makers might choose to increase or decrease mitigation measures, depending on their objectives. There were 4 key findings.

First, the local incidence thresholds for adding or removing mitigation (on-ramps and off-ramps) depend on the objective that the school community seeks to achieve. When the objective is to minimize the probability of any in-school transmission, thresholds are much lower than when the objective is to keep the number of additional cases less than a given level (Figure 3). This result is intuitive, but the model provides a sense of the magnitude of this difference. Additionally, many incidence thresholds identified in this analysis are low relative to historic and current COVID-19 incidence in many districts across the United States, suggesting that even with high rates of vaccination, depending on their goals, communities may continue to find value in measures such as masking and ventilation until incidence decreases.

Second, these on-ramps and off-ramps are highly dependent on the effectiveness of each type of mitigation, which can vary across contexts and individual school settings. We evaluated a wide range of effectiveness: 20% to 40% risk reduction for simple ventilation and handwashing, 60% to 80% for ventilation and handwashing plus universal indoor masking, and 90% to 100% for the full multilayered mitigation packages often used in 2020 to 2021. Data on these measures are limited, and these ranges are uncertain; schools may be able to assess where they fall within these ranges based on adherence to past mitigation measures and the resources available. Screening of asymptomatic students, educators, and staff may be another tool to support more permissive off-ramps when unmasking is strongly desired. Weekly screening decreased the additional modeled cases associated with mitigation relaxation compared with only diagnostic testing (Figure 4A), approximately doubling the local incidence thresholds for removing other mitigation measures (eTable 4 in the Supplement), but schools need to weigh the cost of screening against these benefits. Weekly screening after unmasking may also provide valuable information about the consequences of this change in an individual school.

Third, student vaccination coverage was associated with a very substantial shift in incidence-based thresholds; less intensive in-school mitigation measures are needed to maintain lower transmission as student vaccination rates increase (Figure 3). The incidence-based thresholds were also sensitive to vaccine effectiveness. The higher modeled values (eg, 90%) may more accurately reflect recent vaccination for children (before waning vaccine effectiveness occurs)⁶⁰ and/or booster vaccinations for adults⁶¹ with the Delta variant, and the lower values (eg, 25% and 50%) may reflect values in the future, with further waning or new variants, including Omicron (eTables 5-7 in the Supplement).⁶² Importantly, substantial racial and economic disparities are quickly emerging in elementary student vaccination rates, mirroring these disparities in adults.^63,64 These results demonstrate that efforts to ensure equitable access to accurate information, trustworthy messengers, and convenient vaccination sites will be critical to ensuring equitable application or relaxation of mitigation measures in schools.

Fourth, many policy makers have suggested that the objective of COVID-19 policies should be reducing hospitalizations and deaths, rather than numbers of infections or reported cases, noting that widespread availability of vaccination will reduce morbidity and mortality when infections occur.^44,65 Although our approach to estimating hospitalization rates is approximate, it provides insight into the order of magnitude of potential hospitalizations resulting from different levels of mitigation effectiveness. To achieve even a fairly permissive objective of avoiding 5 additional hospitalizations per 100 000 individuals per month, some scenarios permit unmasking only at incidence thresholds below 30 observed cases per 100 000 residents per day (if removing mitigation is associated with moderate or large decreases in effectiveness, with low student vaccination uptake). In scenarios with high student vaccination rates or smaller incremental mitigation effectiveness, unmasking could achieve this goal at high levels of local incidence (ie, >45 cases per 100 000 per day).

These results should be interpreted in the context of model limitations. First, several key data inputs were highly uncertain, including the effectiveness of individual mitigation interventions, proportions of all SARS-CoV-2 infections that are observed and reported, and hospitalization risks. To account for this uncertainty, we presented results across a range of mitigation effectiveness assumptions; incidence-based thresholds can be adjusted to reflect different proportions detected through simple multiplication (eg, to convert base-case assumption of 33% detection to 50% detection, incidence thresholds can be multiplied by 1.5); and the hospitalization rate objectives (eg, keep additional hospitalizations below 5 per 100 000 individuals per month) can be multiplied by similar conversion factors. COVID-19 incidence data at the most local level available (eg, school or city or town), including data from high-uptake asymptomatic screening, could provide the best information to inform the connection between observed and actual case counts. Additionally, this analysis focused on students, educators, staff, and their household members; additional downstream effects in the nonschool community are not captured (eg, infections from students to family outside the immediate household), which is especially relevant for the hospitalization rate results, because downstream infections in older individuals are more likely to result in hospitalizations compared with those in the relatively younger immediate school community.

In this modeling study of a simulated elementary school and the risks of in-school SARS-CoV-2 transmission, we found that the risks of transmission and resulting infections among students, educators, staff, and their household members are high when a highly infectious variant predominates and students are unvaccinated. Mitigation measures or vaccinations for students substantially reduced these modeled risks. Appropriate on-ramps and off-ramps for in-school mitigation depend on the objectives that policy makers seek to achieve. These findings provide a framework for responsive plans in which mitigation is deployed based on local COVID-19 incidence and vaccine uptake. For evidence-based COVID-19 policy, school policy makers must define clear goals and select thresholds to add or remove mitigation measures based on these goals.

Accepted for Publication: December 17, 2021.

Published: February 14, 2022. doi:10.1001/jamanetworkopen.2021.47827

Correction: This article was corrected on August 25, 2022, to fix errors in the Results, Discussion, Figure 3, and the Supplement. It was previously corrected on March 1, 2022, to fix an error in Figure 3.

Open Access: This is an open access article distributed under the terms of the CC-BY License. © 2022 Giardina J et al. JAMA Network Open.

Corresponding Author: Andrea L. Ciaranello, MD, MPH, Division of Infectious Disease and Medical Practice Evaluation center, Massachusetts General Hospital, 55 Fruit St, Boston, MA 02114 (aciaranello@mgh.harvard.edu).

Author Contributions: Mr Giardina had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.

Concept and design: All authors.

Acquisition, analysis, or interpretation of data: All authors.

Drafting of the manuscript: Giardina, Ciaranello.

Critical revision of the manuscript for important intellectual content: All authors.

Statistical analysis: Giardina, Ciaranello.

Obtained funding: Salomon.

Administrative, technical, or material support: Bilinski, Ciaranello.

Supervision: Bilinski, Linas, Ciaranello.

Conflict of Interest Disclosures: Mr Giardina reported receiving grants from Facebook as an unrestricted gift to Harvard University during the conduct of the study and grants from the Agency for Healthcare Research and Quality, Harvard University, and the Center for Health Decision Science (Harvard T.H. Chan School of Public Health) outside the submitted work. Dr Bilinski reported receiving grants from the US Centers for Disease Control and Prevention through the Council of State and Territorial Epidemiologists and Facebook during the conduct of the study. Dr Fitzpatrick reported receiving grants from the National Institutes of Health during the conduct of the study. Dr Linas reported receiving grants from the National Institute on Drug Abuse, the US Centers for Disease Control and Prevention, and the National Institute of Allergy and Infectious Disease during the conduct of the study. Dr Salomon reported receiving grants from the US Centers for Disease Control and Prevention through the Council of State and Territorial Epidemiologists and from the National Institute on Drug Abuse during the conduct of the study. Dr Ciaranello reported receiving grants from the National Institutes of Health during the conduct of the study. No other disclosures were reported.

Funding/Support: The authors were supported by the US Centers for Disease Control and Prevention though the Council of State and Territorial Epidemiologists (grant No. NU38OT000297-02 to Drs Bilinski and Salomon), the National Institute of Allergy and Infectious Diseases (grant No. R37AI058736-16S1 to Dr Ciaranello; grant No. K01AI141576 to Dr Fitzpatrick; and grant No. K08127908 to Dr Kendall), the National Institute on Drug Abuse (grant No. 3R37DA01561217S1 to Dr Salomon), and Facebook (unrestricted gift to Mr Giardina and Drs Bilinski and Salomon).

Role of the Funder/Sponsor: The funders had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

Disclaimer: The article’s contents are solely the responsibility of the authors and do not represent the official views of the funders.

Additional Contributions: We are grateful to Dr Sandra B. Nelson, MD (Massachusetts General Hospital) and Dr Shira Doron, MD (Tufts Medical Center) for expert opinion on mitigation measure effectiveness. Neither individual was compensated for their support on this work.