Box 1. Our modeling framework—the multi-state discrete time SEIR infection model stratified by cohort and day of infection.

Cohorts normally correspond to student grades but they could also include part of each grade and school staff. Variables are defined in Table 1 and are dependent on time t. Index i runs over all cohorts in the school and index d ∈{1…df} over the days from day 1 after infection to recovery. Return rates from isolation at day rd(p) depend on symptom isolation policy p, δ1,d is the Kronecker delta function (=1 if d is 1, and otherwise zero). ci,j is the connectivity between cohorts i and j and sd is the viral shedding at day d of infection. Estimates for the parameters are in Appendix Tables S2, S3 and S4.

ΔSi = −bSiλi, where λi = Σj,dci,jsdIj,d is the force of infection

Hi,d = (1 − rd(p)) (Hi,d − 1 + Ii,d − 1) (1 − δ1,d)

Ii,d = rd(p) (Hi,d − 1 + Ii,d − 1) (1 − δ1,d) + δ1,dbSiλi

$\mathrm{\Delta }{R}_i=H_{i,d_f}+I_{i,d_f}$