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Modeling SARS-CoV2 spread in a classroom setting

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This document was authored by the EpiCenter for Disease Dynamics, One Health Institute, School of Veterinary Medicine, University of California, Davis. 
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Summary

Implementing preventive measures, such as vaccination, masking, and frequent scheduled testing, will greatly reduce the risk of onward SARS-CoV-2 transmission in the indoor classroom setting. Here, we modeled the risk of transmission if a person infected with SARS-CoV-2 entered a 500 person classroom under several different risk mitigation scenarios. Assuming masking and testing compliance (every 14 days for vaccinated, every 4 days for non-vaccinated and then isolation if positive) and that 90% of the other people in the classroom have been vaccinated and that the vaccines used have 90% efficacy, model results show that the preventive measures substantively reduced the risk of an outbreak resulting from contact in the classroom. Under conditions with these preventive measures, 93% of the time that an infected person comes to a large classroom, no new cases occur throughout the quarter from that person’s infection. Among the 7% of times that an infected person does infect others in a large classroom setting, the peak number of cases is approximately only two others out of a class of 500 students. These models should be re-evaluated under conditions for lesser vaccine efficacy, especially in the event that vaccine efficacy has waned over time in the population, or the efficacy is reduced against new SARS-CoV-2 variants. Additionally, this model does not account for transmission outside of this one classroom, nor variability in the number of people entering a single classroom with SARS-CoV-2, which would be informed by prevalence of SARS-CoV-2 in the community.


Approach

We developed an agent-based model with stochastic transmission to understand the spread of SARS-CoV2 in the classroom setting. With this agent-based model, an individual student was modeled explicitly to enable variation in individual behavior and account for heterogeneity in a small population. The following model assumptions and initial conditions were used to setup simulations and preliminary results:

  • Disease progression was represented by four health states - susceptible (S), exposed (E), infected and infectious (I), and recovered or immune, not infectious (R) to form the SEIR model structure.
  • We assumed that transmission occurs only during interactions that occur between students in the class. Disease transmission between infectious and susceptible students was modeled to take place only on “class days” (i.e., days of the week the classes were assumed to take place).
  • Modeling contacts: The number of contacts for an individual student was randomly selected from a Poisson distribution with a specified rate. Figure 1 shows a histogram of randomly generated Poisson distribution representing the number of contacts of 500 students in a class.
Figure 1: Histogram of randomly generated Poisson distribution representing a number of contacts of 500 students in a class.
Figure 1: Histogram of randomly generated Poisson distribution representing a number of contacts of 500 students in a class.

 

  • Modeling an infection event: Infection event for a susceptible individual i, was modeled
〖infection event〗_(i,t)  ~Bin(〖# infectious contacts〗_(i,t)  ×probability of infection) Where,
  • Modeling vaccination: We assumed that vaccination efficacy is 90%, meaning the chances of infection are reduced by 90% if a person is vaccinated. Hence, the chances of an infection event as represented by equation 2
〖infection event〗_(i,t)  ~Bin(〖# infectious conctats〗_(i,t)×probability of infection ×(1-vaccine efficacy))

  • Modeling testing: While modeling testing scenarios, we assumed that each vaccinated individual would get tested every 14 days, while each non-vaccinated individual would get tested every 4 days. If they are detected positive, i.e., health state exposed (E) or infected (I), they will not be attending classes and will rejoin classes after they are detected negative after 10 days.

Initial conditions and model parameters

Initial conditions and model parameters are presented below in Table 1. We ran 100 stochastic simulations of the model. Two key model outputs were followed to understand SARS-CoV2 progression in the classroom. Firstly, the peak number of cases reported in the outbreak, and secondly, the number of times the outbreak ended (outbreak extinctions) after the introduction.

Table 1: Initial conditions and model parameters used for simulation of SARS-COV2 spread in a classroom.

Model parameter Description value source
N number of students 500  
Class days days in the week when the in-person class will occur Monday, Wednesday, Friday  
Class duration course period (time-period for model simulation) 90 days  
Vaccination rate % Students vaccinated 90%  
Vaccine efficacy Efficacy of vaccine in reducing chances of getting infected post an infectious contact 90%  
Initial infection number of individuals infected at the start of the outbreak 1 individual  
Latent period period of asymptomatic transmission (E to I) 4 days (Getz et al. 2021)
Recovery period period of symptomatic recovery after (I to R) 5 days (Getz et al. 2021)
Stochastic simulations Number of stochastic simulations 100  

Results

Scenario 1: No Vaccination and no other preventive measures (masks and social distancing):

Number of stochastic outbreak extinctions: 19

Figure 2: Number of predicted SARS-COV2 infected individuals in a classroom. The scenario represents the number of infected individuals without any vaccination and preventive measures such as masking and social distancing. Grey lines show individual stochastic simulations, and the red line shows the mean of all 100 stochastic simulations.
Figure 2: Number of predicted SARS-COV2 infected individuals in a classroom. The scenario represents the number of infected individuals without any vaccination and preventive measures such as masking and social distancing. Grey lines show individual stochastic simulations, and the red line shows the mean of all 100 stochastic simulations.

 

Scenario 2: 90% vaccination and no other preventive measures (such as masks and social distancing):

Number of stochastic outbreak extinctions: 38

Figure 3: Number of predicted SARS-COV2 infected individuals in a classroom. The scenario represents the number of infected individuals with 90% and no preventive measures such as masking and social distancing. Grey lines show individual stochastic simulations, and the red line shows the mean of all 100 stochastic simulations.
Figure 3: Number of predicted SARS-COV2 infected individuals in a classroom. The scenario represents the number of infected individuals with 90% and no preventive measures such as masking and social distancing. Grey lines show individual stochastic simulations, and the red line shows the mean of all 100 stochastic simulations.

 

Scenario 3: 90% vaccination and preventive measures in place (masks only):

Number of stochastic outbreak extinctions: 76

Figure 4: Number of predicted SARS-COV2 infected individuals in a classroom. The scenario represents the number of infected individuals with 90% and preventive measures such as masking and but no social distancing. Grey lines show individual stochastic simulations, and the red line shows the mean of all 100 stochastic simulations.
Figure 4: Number of predicted SARS-COV2 infected individuals in a classroom. The scenario represents the number of infected individuals with 90% and preventive measures such as masking and but no social distancing. Grey lines show individual stochastic simulations, and the red line shows the mean of all 100 stochastic simulations.

 

Scenario 4: 90% vaccination and preventive measures in place (masks and social distancing with half the number of contacts):

Number of stochastic die-offs (outbreak extinctions): 89

Figure 5: Number of predicted SARS-COV2 infected individuals in a classroom. The scenario represents the number of infected individuals with 90% and preventive measures such as masking and social distancing with reduced contact. Grey lines show individual stochastic simulations, and the red line shows the mean of all 100 stochastic simulations.
Figure 5: Number of predicted SARS-COV2 infected individuals in a classroom. The scenario represents the number of infected individuals with 90% and preventive measures such as masking and social distancing with reduced contact. Grey lines show individual stochastic simulations, and the red line shows the mean of all 100 stochastic simulations.

 

Scenario 5: 90% vaccination and testing (every 14 days for vaccinated, every 4 days for non-vaccinated), and preventive measures in place (masks only):

Number of stochastic die-offs (outbreak extinctions): 93

Figure 6: Number of predicted SARS-COV2 infected individuals in a classroom. The scenario represents the number of infected individuals with 90% and preventive measures such as masking and implementation of a testing regimen. Grey lines show individual stochastic simulations, and the red line shows the mean of all 100 stochastic simulations.
Figure 6: Number of predicted SARS-COV2 infected individuals in a classroom. The scenario represents the number of infected individuals with 90% and preventive measures such as masking and implementation of a testing regimen. Grey lines show individual stochastic simulations, and the red line shows the mean of all 100 stochastic simulations.

Key takeaways

Reduced chances of classroom outbreak with preventive measures: Reducing contacts and implementing preventive measures such as vaccination and masking will drastically reduce the risk of onward SARS-CoV-2 transmission within a classroom. This is represented by the very low number of new cases when an outbreak did ensue, as well as the number of times an introduction ended before causing any new cases (stochastic outbreak extinctions) as shown in Table 2. Stochastic outbreak extinctions are a great way of understanding the herd immunity in a small population. For scenario 1, without any vaccines and preventive measures, only 19 introductions of the infection died naturally without causing an outbreak. In contrast, for scenario 3 with vaccination and preventive measures in place, 76 introductions ended without causing any new secondary cases.

Table 2: Summary of model outputs for four simulated scenarios.

Scenarios Vaccination coverage Preventive measures Testing The average number of contacts Stochastic outbreak extinctions Outbreak peaks (cases)
Scenario 1 0% No No 10 19 >200
Scenario 2 90% No No 10 38 60
Scenario 3 90% Yes* No 10 76 approx. 10
Scenario 4 90% Yes* No 5 89 approx. 3
Scenario 5 90% Yes* Yes 10 93 approx. 2

*  Modeled with a reduced probability of infection

As shown in table 2, implementing preventive measures will drastically reduce the size of possible outbreaks in the classroom when onward transmission occurs. In the campus’ planned scenario 5 (with vaccination, preventive measures such as masking, and testing), very few onward transmission events occurred in the class.

Because infection transmission was modelled to only occur during class hours, closer inspection of scenarios 1 and 2 show spikes in infected cases on weekdays when the classes take place. Further exploration of distancing class days and optimizing testing strategies around days when classes are planned to take place would help to reduce the chances of an outbreak and further propagation.

Implementation of masking, vaccination, and testing requirements will be important to achieve ideal situations. Reducing the number of close contacts that occur in the classroom, by identifying places where unnecessary crowding might happen, can also minimize risk. However, airborne transmission can make social distancing less effective in the indoor classroom setting, so scenario 5 might be most likely.

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Pranav Pandit, B.V.Sc. & A.H., M.P.V.M, Ph.D
Christine K Johnson, VMD, MPVM, PhD
EpiCenter for Disease Dynamics
One Health Institute, School of Veterinary Medicine
University of California, Davis


Reference

Getz WM, Salter R, Vissat LL, and Horvitz N. 2021. A versatile web app for identifying the drivers of COVID-19 epidemics. Journal of Translational Medicine 19:1-20.