Assessing the impact of SARS-CoV-2 prevention measures in Austrian schools using agent-based simulations and cluster tracing data

As SARS-CoV-2 becomes endemic, safely returning teachers and students to schools requires evidence on school-specific transmission dynamics and evaluation of non-pharmaceutical interventions (NPIs). Prior evidence indicates relatively low transmission in schools, especially among younger students, though sizeable outbreaks have occurred in secondary schools and during high community incidence. The delta variant’s higher transmissibility and shorter incubation period increase challenges, particularly where children are unvaccinated. Countries deploy masks, class size reductions, ventilation, and antigen (AG) screening tests; modelling suggests frequent, rapid-turnaround testing can offset lower sensitivity. Evidence on the effectiveness of combinations of measures under delta and partial vaccination is limited, and many models lack detailed, large-scale cluster data. This study develops and calibrates an agent-based model to Austrian school clusters to assess the effectiveness of NPIs and vaccination across school types, aiming to inform evidence-based policies for keeping schools open under controllable risk.

The paper summarizes literature showing: relatively low in-school transmission overall with younger children contributing less to spread; reports of notable outbreaks in secondary schools during high community transmission; delta variant associated with increased transmissibility and shorter incubation time; widespread implementation of NPIs in schools including masks, ventilation, cohorting/class size reduction, and screening via antigen tests; modelling evidence that AG test frequency and rapid turnaround can outweigh lower sensitivity. Prior descriptions of school clusters often involve small numbers or lack clear attribution of in-school vs out-of-school transmission, and existing sophisticated models often lack comprehensive, detailed cluster data for calibration. These gaps motivate the present calibrated agent-based approach adapted to variant characteristics.

Design: Agent-based epidemiological model coupling in-host viral dynamics with day-dependent, multi-relational contact networks for Austrian schools. Agents include students, teachers, and household members. States: susceptible (S), exposed (E), infectious (I; symptomatic I2 or asymptomatic I1), recovered (R), quarantined (X). Transitions follow distributions for exposure duration, incubation period, and infection duration; viral load-dependent infectivity is modelled with a trapezoid function over time. Data and calibration: Model calibrated to 616 Austrian school clusters (calendar weeks 36–45, 2020) including 2,822 student-cases and 676 teacher-cases (464 source cases; 3,034 in-school transmissions). School types: primary, lower secondary, upper secondary, and secondary (with/without daycare). Calibration targets: (i) realistic cluster size distributions, (ii) student-to-teacher infection ratios. Inputs include empirically observed age-specific symptomatic proportions and teacher-to-student source ratios by age. Household base transmission risk β calibrated to reproduce a cumulative adult household secondary attack risk of 37.8% for the original strain, resulting in β≈7.37% per day; for delta, household transmission risk multiplied by 2.25; incubation period set to 4.4±1.9 days and latent period 3.0±1.9 days; infection duration 10.9±4.0 days. Contact networks: Constructed from Austrian school statistics and interviews; include class interactions, teacher-student teaching contacts, daycare mixing across classes, teacher-teacher meetings, team-teaching, households and sibling links. Networks are dynamic (weekday schedule) and multi-relational (household vs school contact intensities). Typical school sizes (classes, students per class, teachers) per type are specified; secondary schools have larger, denser networks and higher teacher connectivity than primary schools. Transmission probability per contact is a Bernoulli trial with base risk modified by mechanisms qi: contact type (household vs school), age of transmitter and receiver (linear decrease in risk below age 18 with slope c_age), infection progression (time since exposure), symptoms (reduction for asymptomatic), mask wearing (exhale/inhale reductions), ventilation (air exchange), and immunization (vaccination). Calibrated school contact risk reduction c_contact≈0.30 (i.e., 70% reduction vs household); c_age≈−0.005 (risk and susceptibility reduced by 0.5% per year below 18). Sensitivity analyses on c_contact and c_age show limited impact relative to NPI parameter uncertainties. NPIs evaluated: (i) room ventilation (once/hour; ~64% transmission reduction), (ii) surgical mask use by teachers/students during lessons (50% exhale; 30% inhale reductions), (iii) class size reduction via alternating attendance (~50% of students present on alternating days), (iv) school entry screening using antigen tests (once or twice weekly), on top of baseline test-trace-isolate (TTI) with PCR for symptomatic cases. Testing/tracing assumptions reflect calibration period (background screens with PCR then; in other simulations only household quarantine on positives). AG test sensitivity modelled as time-window step function yielding overall ~0.45 sensitivity; PCR sensitivity from day 4–11 post-exposure; AG results same-day; PCR results with 1–2 day delay. Vaccination scenarios: Scenario I: 80% teachers, 60% household members, 0% students vaccinated; Scenario II: as I plus 50% students vaccinated. Vaccination modelled as 60% reduction in susceptibility upon exposure (no reduction in infectiousness if infected). Vaccination status static within simulations. Outcomes: Cluster size distributions and reproduction number R computed as the average number of secondary infections caused by the source case. Scenarios examined across school types, NPIs singly and in combinations, with sensitivity analyses varying NPI effectiveness, participation rates, and between-class friendship contacts (0–40%). Online visualization tool provided for stakeholder exploration (educational purposes).

Empirical cluster data: - 616 clusters with ≥1 in-school transmission, involving 9,232 cases; 3,498 school-cluster cases (2,822 students; 676 teachers), 464 source cases, and 3,034 in-school transmissions. - Distribution of cluster sizes: 40% had size 2; 49% size 3–9; 8% size 10–19; 3% size ≥20. - Student-source case share lowest in primary (6%), higher in lower secondary (43%), secondary (64%), upper secondary (82%). - Clusters with teacher source cases were larger (mean 5.7) than with student sources (mean 4.4). Calibration and transmission parameters: - School contacts have ~70% lower per-day transmission risk than household contacts (c_contact≈0.30). - Children’s transmission risk and susceptibility decrease linearly with age below 18 (c_age≈−0.005), implying ~6% lower risk for a 6-year-old vs an 18-year-old. No-mitigation baseline (TTI only, no vaccinations; delta parameters): - Average cluster sizes assuming typical school sizes: primary 69 (75th: 127; 90th: 206), lower secondary 211 (303, 3014), secondary overall 1073 (1402, 1420). - Reproduction numbers R (student source): primary 2.6 (SD 2.1), lower secondary 3.2 (2.4), secondary 3.6 (2.7). Teacher-source R: primary 4.4 (2.9), lower secondary 8.1 (4.5), secondary 9.8 (6.1). Effectiveness of single NPIs (no vaccination): - AG screening is most effective. Testing students twice weekly reduces cluster sizes to: primary student-source 3 (3, 6) [teacher-source 14 (18, 33)]; secondary student-source 128 (5,695) [teacher-source 600 (726, 752)]. Testing teachers twice weekly: primary student-source 27 (39, 79) [teacher-source 13 (6, 45)]; secondary student-source 762 (1174, 1218) [teacher-source 503 (1142, 1204)]. - Ventilation (~64% reduction) substantially reduces sizes: primary student-source 6 (7, 14) [teacher-source 9 (11, 22)]; secondary student-source 240 (653, 749) [teacher-source 461 (729, 784)]. - Class size reduction (alternating 50% attendance): primary student-source 6 (5, 13) [teacher-source 14 (19, 34)]; secondary student-source 278 (755, 810) [teacher-source 666 (802, 836)]. - Mask wearing during lessons (50% exhale; 30% inhale): primary student-source 9 (8, 25) [teacher-source 23 (36, 56)]; secondary student-source 438 (1006, 1053) [teacher-source 905 (1041, 1070)]. - Of single NPIs, only twice-weekly testing among students lowers average R below 1 for student-source clusters in primary and lower secondary schools. Otherwise, multiple NPIs are required for R<1. Combinations of NPIs (no vaccination): - Sequentially adding ventilation, masks (teachers then students), and class size reduction yields R<1 only in primary schools without preventive testing (outbreak sizes ~2–4). Other school types generally require preventive testing to reach R<1. - Ventilation + weekly AG testing of both teachers and students achieves R<1 in primary and lower secondary schools for student-source clusters; upper/secondary schools need at least twice-weekly student testing. - Ventilation + weekly AG testing + masks can control teacher-source clusters across all school types. - Ventilation + testing + class size reduction is less effective than adding masks (e.g., teacher-source in secondary: average size 3 (4, 8) with R=1.2 (SD 1.5)). - Combining all NPIs results in R<1 across all school types and for both source types. Sensitivity (conservative assumptions; reduced NPI effectiveness, partial participation, extra between-class contacts): - Reduced effectiveness leads to exponential increases in cluster sizes. With weekly testing of teachers and students, outbreak sizes increase >270-fold in secondary and 17-fold in primary schools vs baseline. Testing twice weekly + class size reduction increases average sizes ~4-fold (primary) and ~157-fold (secondary) for student-source clusters. Mask-combination strategies show smaller increases (1.7–3.5× primary; 27–59× secondary). Under these conservative assumptions without vaccination, no combination achieves R<1, even in primary schools. Vaccination scenarios (with conservative NPI assumptions): - Scenario I (80% teachers, 60% family, 0% students vaccinated): ventilation + masks + class size reduction achieves R<1 for student-source clusters in primary and lower secondary; R>1 persists in upper/secondary and for teacher sources. Example outbreak sizes: primary 2 (3, 5) [teacher 4 (5, 8)]; secondary 4 (4, 8) [teacher 12 (14, 28)]. - Scenario II (Scenario I plus 50% students vaccinated): implementing all NPIs yields R<1 for all school types and sources except teacher-source in secondary (R≈1.3–1.4). Outbreak sizes range from primary 2 (2, 3) [teacher 2 (2, 4)] to secondary 2 (2, 4) [teacher 4 (5, 8)]. Additional observations: - Household infections per school case decline with vaccination: no-mitigation ~1.10 (primary) and 1.01 (secondary); Scenario I ~0.39 and 0.35. - Secondary schools have denser and larger contact networks (e.g., average degrees: primary students 23.6, teachers 43.1; secondary students 33.6, teachers 99.6), contributing to larger outbreaks; teachers tend to drive larger clusters and higher R due to voice projection, age-related risk, and higher network degree. Policy implication: Primary schools typically require at least two NPIs; secondary schools at least three NPIs, with stringent implementation and vaccination substantially improving control.

The calibrated agent-based model demonstrates that school transmission risk and control differ by school type, contact network structure, and whether a student or teacher is the source. Teachers often drive larger outbreaks due to higher connectivity and behavioral factors (speaking loudly), making teacher-focused mitigation (testing, masking) essential. Single NPIs usually do not suffice, particularly in secondary schools; combining ventilation, masking, class size reduction, and frequent screening is necessary to reduce R below 1. The effectiveness of NPIs is highly sensitive to implementation fidelity and participation—linear decreases in measure efficiency can translate into exponential increases in outbreak sizes—so enforceable, consistently applied measures (e.g., mandatory negative tests, CO2-monitored ventilation) may outperform theoretically stronger but weakly implemented measures. Under conservative assumptions without vaccination, NPIs alone cannot control delta spread; vaccinating teachers, households, and especially students markedly reduces outbreak sizes and enables R<1 with fewer NPIs. Results support targeted, school-type-specific bundles: at least two measures for primary/lower secondary and three for upper/secondary schools, with preventive testing central to control. Findings align with evidence that schools reflect community transmission and that younger children contribute less to spread, while highlighting the critical role of network structure in secondary schools.

Using detailed Austrian cluster data to calibrate an agent-based model, the study quantifies the effectiveness of NPIs and vaccination for controlling SARS-CoV-2 (delta) in schools. Key contributions include: (i) school-type-specific estimates of outbreak sizes and R under various NPIs, (ii) identification of preventive testing as the most impactful single NPI, (iii) demonstration that combinations of measures are required—at least two for primary/lower secondary and at least three for upper/secondary schools—and (iv) evidence that vaccination of teachers, households, and students substantially enhances control, enabling R<1 even with conservative NPI effectiveness. Practical implications stress stringent, enforceable implementation and a focus on teacher-related transmission. Future work could refine NPI effectiveness estimates as new evidence emerges, incorporate dynamic vaccination uptake and waning, variant updates, and extend generalizability assessments beyond Austria. An online visualization tool is provided to support stakeholders in scenario exploration.

- Potential observational biases in cluster data: TTI typically triggered by symptomatic cases; asymptomatic infections (more common in children) may have been under-detected, possibly underestimating student-to-student and student-to-teacher transmissions and influencing age-dependent transmission estimates. - Coarse time resolution (daily time steps) may simplify early infection dynamics, though parameter variability mitigates artifacts. - Simplified agent interactions: limited to predominant school and household contacts; other contacts (e.g., janitorial staff) not modelled due to data scarcity. - Generalizability: calibration based on Austrian clusters and education system; applicability to other countries may vary, though Austrian class sizes and teacher ratios are near EU averages. - NPI effectiveness parameters drawn from preliminary literature; despite sensitivity analyses, uncertainties remain. - Vaccination modelling assumes constant 60% susceptibility reduction, no reduced infectiousness if infected, and static vaccination coverage during simulations; waning immunity and changing uptake are not modelled.