School and community reopening during the COVID-19 pandemic: a mathematical modelling study

Abstract

Operating schools safely during the COVID-19 pandemic requires a balance between health risks and the need for in-person learning. Using demographic and epidemiological data between 31 July and 23 November 2020 from Toronto, Canada, we developed a compartmental transmission model with age, household and setting structure to study the impact of schools reopening in September 2020. The model simulates transmission in the home, community and schools, accounting for differences in infectiousness between adults and children, and accounting for work-from-home and virtual learning. While we found a slight increase in infections among adults (2.2%) and children (4.5%) within the first eight weeks of school reopening, transmission in schools was not the key driver of the virus resurgence in autumn 2020. Rather, it was community spread that determined the outbreak trajectory, primarily due to increases in contact rates among adults in the community after school reopening. Analyses of cross-infection among households, communities and schools revealed that home transmission is crucial for epidemic progression and safely operating schools, while the degree of in-person attendance has a larger impact than other control measures in schools. This study suggests that safe school reopening requires the strict maintenance of public health measures in the community.

Keywords: COVID-19; age structure; community opening; household structure; school reopening; transmission model.

Figure 1.

Transmission model with age and household structure. Panel (a) shows the activity and response of different structured population groups: household, schools and other community. Panel (b) shows a schematic diagram of the dynamics of COVID-19 in Toronto. Solid lines indicate movement between classes. Dashed lines represent the virus transmission routes. All individuals from work-outside-home (in subscript g), work-from-home (in subscript q), C&Y attending school in-person (sc) groups are in different disease states, Susceptible (S_i), Exposed (E_i), Infected (subclinical (A_i), prodromal (I_i1) or with symptoms (I_i2)), Hospitalized (H), Isolated (W), Recovered (R) or Deceased (D). i indicates adults and C&Y population (i = a,c). The individuals in the home are labelled with superscript h, which is the sum of corresponding disease states in all the households. C&Y is children and youth.

Figure 2.

Percent increase in new cases among adults and C&Y under different scenarios, compared with when schools are closed. Per cent increase in new cases two, four, six and eight weeks after schools opened among adults (a) and C&Y (b) compared with a scenario with schools closed with no increases in contacts (blue bars), contacts among children increased by 50% (orange bars) and contacts among adults increased by 10% (yellow bars).

Figure 3.

Scenarios where schools are open or closed after 8 September under different control measures. Daily new cases are reported within the adult (a) and C&Y (b) populations under different transmission levels, scenario 1 (blue), scenario 2 (orange), scenario 3 (green) and scenario 4 (purple) as described in the section on Scenario analysis. The solid and dashed line represents the scenarios of schools open or closed, respectively. Data are reported with yellow dots.

Figure 4.

R_t on 5 October 2020, with schools open, under varying household and community transmission risk. (a,c) Adult population; (b,d) children and youth (C&Y) population. Red star represents the level of phase 2; 5 October 2020 is the date of four weeks after school opening.

Figure 5.

PRCC plots of transmission-related parameters on new cases among (a) adults, (b) C&Y and (c) C&Y in school. $c_{aa}$, $c_{ac}$ and $c_{cc}$ denotes the contact rate of adults–adults, adults–C&Y and C&Y–C&Y in the community. ${\beta }_g$ represents probability of transmission per contact among adults in the community. $q_{g2}$ is the quarantine rate of symptomatic infected adults. ${\theta }_i$ is the isolation rate of symptomatic adults' infection. a, proportion of infected with prodromal infection (1−a, the proportion of asymptomatic (subclinical) infection). $q_{sc}$ is the quarantine rate of symptomatic infected C&Y in the school. η is efficiency of self-screening procedures for detecting infected C&Y without symptoms. a_r is the proportion of C&Y attending in-person education. nh is the cohort size in the school.