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Estimating the effect of timetabling decisions on the spread of SARS-CoV-2 in medium-to-large engineering schools in Canada: an agent-based modelling study

Robert W. Brennan, Nancy Nelson and Robyn Paul
December 21, 2021 9 (4) E1252-E1259; DOI: https://doi.org/10.9778/cmajo.20200280
Robert W. Brennan
Department of Mechanical and Manufacturing Engineering (Brennan, Paul), University of Calgary, Calgary, Alta.; Department of Engineering and Information Technology (Nelson), Conestoga University, Cambridge, Ont.
PhD
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Nancy Nelson
Department of Mechanical and Manufacturing Engineering (Brennan, Paul), University of Calgary, Calgary, Alta.; Department of Engineering and Information Technology (Nelson), Conestoga University, Cambridge, Ont.
MSc
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Robyn Paul
Department of Mechanical and Manufacturing Engineering (Brennan, Paul), University of Calgary, Calgary, Alta.; Department of Engineering and Information Technology (Nelson), Conestoga University, Cambridge, Ont.
MSc
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  • Figure 1:
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    Figure 1:

    Transmission model structure. The boxes represent the health states of students. The arrows represent transitions between health states. Exposed cases can be either isolated or not; isolated cases (right side) represent students who were identified via contact tracing or randomized testing.

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    Figure 2:

    Box plots of the number of students who were infected over a 12.7-week term for different timetabling scenarios (no. of replications = 250). The tutorial or laboratory timetables are represented by no. of sections × size of sections. For example, 2 × 90 weekly represents the timetabling scenario of 2 tutorial or laboratory sections of 90 students each week. We used a population of 180 students for all scenarios. The coloured box represents median and interquartile range (IQR); whiskers the most extreme values within 1.5 times of the IQR beyond the 25th and 75th percentiles; and dots outliers.

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    Figure 3:

    Number of students who were infected and number of students isolated for the 6 × 30 biweekly timetable with contact tracing and testing (means with 95% confidence intervals). Simulations were performed at testing frequencies ranging from 3 students tested per day to 36 students tested per day. From an individual student perspective, this corresponds to 1 test per student per 12-week term to 1 test per student per week, respectively. We also performed a base case of 0 students tested per day.

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    Figure 4:

    Number of students who were infected in the 6 × 30 biweekly timetable with vaccination scenario (partial = 1 dose, full = 2 doses) and weekly testing of nonvaccinated students (means with 95% confidence intervals). The effectiveness was based on a study of 2 SARS-CoV-2 vaccines, BNT162b2 (Pfizer-BioNTech) and ChAdOx1 nCoV-19 (AstraZeneca), against symptomatic disease caused by the B.1.617.2 (Delta) variant. (17)

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    Table 1:

    Model parameters for SARS-CoV-2 transmission

    ParameterMean (95% CI)ModelSource and notes
    Incubation period, d5.08 (4.77–5.39)SampledHe et al.; (10) meta-analysis estimate of the mean incubation time
    Latent period, d2.50FixedTuite et al.; (11) retrospective cohort study estimate of the mean time to exposure to onset of infectiousness
    Time to isolation
     Symptom-based, d4.60 (4.10–5.00)SampledBi et al.; (12) retrospective cohort study estimate of the mean time to isolation
     Contact-based, d1.90 (1.10–2.70)Sampled
    Recovery time, d20.80 (20.10–21.50)SampledBi et al.; (12) retrospective cohort study estimate of the mean recovery time
    Asymptomatic infection rate, %46.00 (18.40–73.60)SampledHe et al.; (10) Meta-analysis estimate of the mean asymptomatic infection rate (10)
    Attack rate, %6.10 (3.00–12.10)SampledKoh et al.; (13) retrospective cohort study estimate of the mean attack rate. We used the estimate for 20–29 years of age.
    Secondary attack rate, %4.00 (2.80–5.20)FixedKoh et al.; (13) meta-analysis estimate of the mean secondary attack rate (SAR). We used the nonhousehold SAR and the ratio of symptomatic versus asymptomatic SAR to calculate the probability of virus spread for symptomatic and nonsymptomatic contacts, respectively.
    Outside transmission, cases/100 000/wk153FixedWe performed the calculation of the probability of outside transmission on a daily basis based on the incident rate reported by the Government of Alberta; (14) population statistics were taken from Statistics Canada. (15)
    Test duration, d2FixedGovernment of Alberta; (14) less than 2 days from swab collection to test result (1 d for the laboratory to receive the swab and 13 h for the result)
    Isolation period, d14FixedGovernment of Alberta (16) mandatory isolation guideline
    Vaccine effectiveness (1 dose), %30.70 (25.20–35.70)Fixed (mean)Lopez Bernal et al. (17) Effectiveness of BNT162b2 (Pfizer-BioNTech) and ChAdOx1 nCoV-19 (AstraZeneca) vaccination against symptomatic disease caused by the B.1.617.2 (delta) variant.
    Vaccine effectiveness (2 doses), %79.60 (76.70–82.10)Fixed (mean)Lopez Bernal et al. (17) Effectiveness of BNT162b2 (Pfizer-BioNTech) and ChAdOx1 nCoV-19 (AstraZeneca) vaccination against symptomatic disease caused by the B.1.617.2 (Delta) variant.
    Initial seeding1 studentFixedWe assumed an initial outbreak of 1 student who acquired SARS-CoV-2 infection.
    • Note: CI = confidence interval. The “model” column indicates whether a sampled or a fixed value was used in the model. We took all samples from the Gaussian distribution. Descriptions of the distribution parameters are provided in Appendix 1A, available at www.cmajopen.ca/content/9/4/E1252/suppl/DC1.

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    Table 2:

    Number of students infected, using alternative surveillance policies with online lectures in the model

    TimetableSurveillance typeMean ± SD95% CI
    Weekly tutorial or laboratory section
     1 × 180Symptom143.97 ± 38.01139.23–148.46
     2 × 90Symptom101.68 ± 38.3896.90–106.46
     3 × 60Symptom88.40 ± 34.7384.07–92.72
     1 × 180Contact18.41 ± 11.1717.02–19.80
     2 × 90Contact16.81 ± 10.2115.54–18.08
     3 × 60Contact17.70 ± 10.5416.39–19.02
    Biweekly tutorial or laboratory section
     2 × 90Symptom23.62 ± 13.3421.96–25.29
     4 × 45Symptom22.78 ± 13.3621.12–24.45
     6 × 30Symptom22.50 ± 12.5220.83–24.16
     2 × 90Contact11.96 ± 6.7611.11–12.80
     4 × 45Contact11.70 ± 6.5310.89–12.52
     6 × 30Contact12.12 ± 6.2011.34–12.89
    • Note: CI = confidence interval, SD = standard deviation. Tutorial or laboratory timetables are represented by no. of sections × size of sections. For example, 2 × 90 weekly represents the timetabling scenario with 2 tutorial or laboratory sections of 90 students each week.

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CMAJ Open: 9 (4)
Vol. 9, Issue 4
1 Oct 2021
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Estimating the effect of timetabling decisions on the spread of SARS-CoV-2 in medium-to-large engineering schools in Canada: an agent-based modelling study
Robert W. Brennan, Nancy Nelson, Robyn Paul
Oct 2021, 9 (4) E1252-E1259; DOI: 10.9778/cmajo.20200280

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Estimating the effect of timetabling decisions on the spread of SARS-CoV-2 in medium-to-large engineering schools in Canada: an agent-based modelling study
Robert W. Brennan, Nancy Nelson, Robyn Paul
Oct 2021, 9 (4) E1252-E1259; DOI: 10.9778/cmajo.20200280
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