Model-based assessment of SARS-CoV-2 Delta variant transmission dynamics within partially vaccinated K-12 school populations

Abstract

Background: We examined school reopening policies amidst ongoing transmission of the highly transmissible Delta variant, accounting for vaccination among individuals ≥12 years.

Methods: We collected data on social contacts among school-aged children in the California Bay Area and developed an individual-based transmission model to simulate transmission of the Delta variant of SARS-CoV-2 in schools. We evaluated the additional infections in students and teachers/staff resulting over a 128-day semester from in-school instruction compared to remote instruction when various NPIs (mask use, cohorts, and weekly testing of students/teachers) were implemented, across various community-wide vaccination coverages (50%, 60%, 70%), and student (≥12 years) and teacher/staff vaccination coverages (50% - 95%).

Findings: At 70% vaccination coverage, universal masking reduced infections by >57% among students. Masking plus 70% vaccination coverage enabled achievement of <50 excess cases per 1,000 students/teachers, but stricter risk tolerances, such as <25 excess infections per 1,000 students/teachers, required a cohort approach in elementary and middle school populations. In the absence of NPIs, increasing the vaccination coverage of community members from 50% to 70% or elementary teachers from 70% to 95% reduced the excess rate of infection among elementary school students attributable to school transmission by 24% and 37%, respectively.

Interpretations: Amidst Delta variant circulation, we found that schools are not inherently low risk, yet can be made so with high community vaccination coverages and masking. Vaccination of adults protects unvaccinated children.

Funding: National Science Foundation grant no. 2032210; National Institutes of Health grant nos. R01AI125842 and R01AI148336; MIDAS Coordination Center (MIDASSUP2020-4).

Keywords: Alpha; COVID-19; Delta; SARS-CoV-2; masks; schools; transmission model; vaccination.

Figure 1

Model schematic (a) Schematic of the agent-based susceptible–exposed–infected–recovered (SEIR) model. Individuals, i, move through states S, susceptible; E, exposed; A, asymptomatic; C, symptomatic, will recover; H1, symptomatic and will recover, not yet hospitalized; H2, hospitalized and will recover; D1, symptomatic, not yet hospitalized; D2, hospitalized and will die; R, recovered; M, dead; and V, vaccinated. The force of infection, λ, defines movement from S to E; η represents vaccine effectiveness; and θ, vaccination coverage among subgroup to which individual i belongs. After an agent enters the exposed class, they enter along their predetermined disease progression track, with waiting times between stage progression drawn from a Weibull distribution. V. (b) Schematic of the conditional probabilities by which agents are assigned a predetermined track. Figure is adapted, with permission, from [15].

Figure 2

Effect of non-pharmaceutical interventions. We examined the effect of three non-pharmaceutical interventions across three levels of community vaccination coverage (50%, 60%, 70%), assuming that vaccination coverage within school children 12+ and teachers matches that in the community and the vaccine effectiveness is 77% against infection, 85% against symptomatic infection, and 93% against severe infection. Masks indicate universal masks regardless of vaccination status. We calculated the mean (stars) and median (diamonds) of excess cases per 100 persons attributable to school transmission among population subgroups across 1,000 model realizations. Vertical lines reflect the 89^thpercentile high probability density interval (HPDI).

Figure 3

Share of the excess risk by vaccination status and disease outcome, across various vaccine coverages and effectiveness and populations. Red colors reflect the share of excess infections among unvaccinated persons, while green represents excess infection among vaccinated persons. Dark hues represent severe disease (i.e., needing hospitalization), medium hues represent symptomatic but not severe infection, and light hues represent asymptomatic infection. Hashes on the student and the household members represent infections among unvaccinated individuals who are ineligible for vaccination at the start of the fall 2021 semester (<12 years). The high vaccine effectiveness scenario (panels A, B) models vaccines that are 77% effective against any infection, 85% effective against symptomatic infection, and 93% effective against severe infection. The low vaccine effectiveness scenario (panels C, D) models vaccines that are 41% effective against any infection, 45% effective against symptomatic infection, and 49% effective against severe infection.

Figure 4

Effect of increasing within-school vaccination coverage. We examined the effect of increasing vaccination coverage among school populations, in the absence of additional non-pharmaceutical interventions, and holding community and within-school vaccination coverage of the 12+ population at 70%. We calculated the mean (stars) and median (diamonds) of excess risk per 100 persons attributable to school transmission among population subgroups across 1,000 model realizations. Vertical lines reflect the 89^thpercentile high probability density interval (HPDI).

Figure 5

Effect of universal masking compared to masking only of unvaccinated individuals. We estimated the additional cases averted in each population by masking the entire student and teacher population, compared to masking only the unvaccinated student and teacher population, in the absence of additional interventions. We held community and within-school vaccination coverage of the 12+ population at 70%, and varied vaccine efficacy (VE). We calculated the mean (stars) and median (diamonds) of excess risk per 100 persons attributable to school transmission among population subgroups across 1,000 model realizations. Vertical lines reflect the 89^thpercentile high probability density interval (HPDI). Shaded bars and right axis reflect the vaccinated percent of the school population, for whom a universal masking rule as compared to a masking rule among the unvaccinated would apply.