Model Overview

The ABM simulates an individual's progression through seven stages:
  1. COVID-19 negative
  2. COVID-19 positive, pre-symtomatic
  3. COVID-19 positive, asymptomatic
  4. COVID-19 positive, symptomatic
  5. Hospitalization
  6. Recovery
  7. Death
Each day, an individual either remains in the current stage or transitions to another stage.
The ABM includes five types of contact between individuals:
  1. Class - interactions within the classroom
  2. Lunch/Recess - interactions at lunch and during recess
  3. Bus - interactions on the school bus
  4. Faculty - interactions during staff meetings
  5. Community - interactions occurring from social interactions outside the school

Re-opening policies

The ABM simulates the spread of COVID-19 under seven different mitigation strategies that aim to reduce COVID-19 transmission within a school. An effective strategy (in terms of infection reduction) would limit within-school transmissions, increasing the proportion of all transmissions that occur outside of (and thus out of the control of) the school.

All scenarios assume 20 percent of students will stay home from school due to COVID concerns. Note: policies C and D are not applicable to non-departmentalized elementary schools.

Policy A: no intervention
A worst-case scenario under which schools fully re-open and operate as if the pandemic had not occurred.

Policy B: daily attendance with precautions
Students wear masks on the bus only, and school staff wear masks at all times. Students interact with other students only in their classes. Lunch is eaten in classrooms. Elementary school students have recess with only their own classmates.

Policy C: daily attendance with precautions and block scheduling
Same as Scenario B, with an additional shift to block scheduling for middle schools and high schools, meaning that each class meets only every other day for double the amount of time.

Policy D: daily attendance with precautions and students staying in one classroom
Same as Scenario B, except the same group of students is kept together for all classes while teachers move between classrooms druing the day. The only contact that students have with other students outside their classs is on the bus.

Policy E: rotating 2 days per week
Same as Scenario B, except that students are divided into two groups, with half coming to school on Mondays and Wednesdays and the other half coming to school on Tuesdays and Thursdays. All students remain at home on Fridays for remote instruction. Reducing the school population by one-half each day is likely to be sufficient to allow 6 feet of distance between desks in most classrooms and cuts in half the number of other students that each student is in contact with.

Policy F: weekly 4-day rotations
Same as Scenario E, except that instead of a daily rotation, the two groups of students are on a weekly rotation. One group of students attends Monday through Thursday in Week 1, and the second group of students attends Monday through Thursday in Week 2.

Policy G: rotating 1 day per week
Students are divided into 5 groups with each group coming to school only 1 day per week, with all other learning conducted at home. This is the only scenario that is sure to reduce daily bus ridership enough to implement the physical distancing suggested by the CDC.


The ABM is based on underlying assumptions about a number of key parameters, including rates of transmission in different contexts and susceptibility probabilities. We have done our best to base these parameters on estimates from the emerging COVID-19 literature, but there is still scarcity in information regarding the spread of COVID-19, especially for children. Further, there is significant uncertainty in identified estimates for transmission and susceptibility rates. For parameters where we could not find reliable estimates in the literature, e.g. for the transmission rates of COVID-19 on school buses, we used rates that seemed pluasible relative to other rates in used in the model.
This app displays the results of an agent based model (ABM) developed to simulate the spread of COVID-19 among students, faculty, and staff at K-12 schools under different approaches to school re-openings.

The ABM results focus on the probable relative effectiveness of different re-opening strategies. In particular, the results illustrate the relative differences in the estimated time it takes for the first five infections to occur in the school population (students, faculty, and staff) for Policies A-G described above. This relative difference ("relative time factor") is measured with respect to a selected "baseline" policy.

Relative time to reach 5 infections

Transmission mode

When considering factors for reopening schools, stakeholders should also take into account issues of equity and the potential for various school policies to have disproportionate impacts on students from families with low income, communities of color, and students with special needs.

For additional details on the underlying model assumptions, please refer to the following memo: Considerations for Reopening Pennsylvania Schools.

Relative time to reach 5 infections

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Transmission mode

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The threat of COVID-19 and the coordinated policy response playing out in real time around the globe are unprecedented. Evidence can help light the path forward. Together with our partners, we’re applying our collective knowledge and experience at the intersection of data, analytics, policy, and practice to help address today’s complex challenges related to COVID-19. Visit our website learn more about relevant resources and examples of our scalable services. Contact for more information or to speak with one of our experts.

Summary and key findings from “Considerations for Reopening Pennsylvania Schools”

In May 2020, the Pennsylvania Department of Education (PDE) approached the Mid-Atlantic Regional Educational Laboratory (REL), led by Mathematica, for analytic support of its effort to produce guidance for the re-opening of school buildings in the midst of the COVID-19 pandemic. The REL partnered with PDE on a three-part project, which included examining emerging evidence on COVID-19’s public-health and educational implications for schools; interviewing a wide range of Pennsylvania stakeholders to assess concerns and challenges related to reopening school buildings; and creating an agent-based computational model to assess likely disease spread among students and school staff under various approaches to reopening school buildings. The findings are summarized in this memo.

The results of this evidence scan should be considered preliminary because of the rapidly emerging and changing evidence available on the public health and educational questions relevant to this review. The findings point toward potentially promising practices that stakeholders can continue to assess as future, more rigorous research becomes available. Key findings are below.

Health risks and COVID-19 transmission

Although the evidence is not conclusive, multiple studies suggest that children, particularly children under age 10, may be less likely to be infected with the virus - which would also make them less likely to spread the disease either symptomatically or asymptomatically.1,2,3 When children do contract the virus, they often have mild symptoms that are similar to other viral respiratory infections.4 Although evidence suggests that the risks to children from COVID-19 are low, recent concern has arisen about the risks from a Multisystem Inflammatory Syndrome in Children (MIS-C) that is associated with COVID-19. This can be a serious condition, but cases are rare and there are very few deaths in reported patients.5

However, staff members and family members of students are likely at greater risk from COVID-19 than children. There is no evidence to suggest that children cannot transmit the disease and the percentage of infected adults who become symptomatic rises with age, as do hospitalizations and fatalities.1,6 While reopening schools may not pose significantly high risk for children, reopening may have riskier consequences for the adults with whom the children interact and the community at large.

Contribution of school closures and reopening to COVID-19 spread

The extent to which school closures have helped to reduce infection spread during the COVID-19 pandemic is not clear and has been subject to considerable debate. Several studies document cases where COVID-19 spread significantly in schools, but the number of school-based spreads represent a small proportion of super spreader events (events that result in multiple infections from a single person).7, 8 However, other studies suggest the school closures have been effective measures to prevent COVID-19 spread and related deaths.9,10

Although the role of schools in COVID-19 transmission is ambiguous, when developing plans for school reopening in the absence of a vaccine, there are various strategies schools should employ to mitigate COVID-19 spread. Schools should consider practices such as physical distancing11, masking11,12, ventilation13, and meeting outdoors14 to reduce the risk of COVID-19 transmission, along with other CDC recommendations.15

Learning loss and remote learning

The closure of schools in spring 2020 is likely to lead to substantial learning loss and may exacerbate existing inequities. Research suggest that students will experience greater learning loss than the typical “summer slide” and that minority students may have greater learning losses than their white classmates.16 Studies also show that this past spring school districts with higher percentages of poverty offered less rigorous remote learning programs and there are concerns about equitable access to devices and reliable broadband to support remote learning for all students.17,18 Although schools had to offer remote-only learning in spring 2020 due to shutdown orders, available research shows that online classes are typically not as effective as in-person classes for most students.19,20 Previous research on remote learning also has not been designed to provide evidence on best practices that could be implemented to help schools and teachers provide effective remote instruction in the current environment.21

Despite the absence of rigorous evidence on best practices in blended and remote learning, research suggests the likely importance of maintaining engagement when students are learning at home and some practices that show promise. If they are learning entirely at home, students are likely to benefit from some synchronous interaction with teachers, which can take place through electronic devices or by phone.21 Effective blended learning programs, such as the hybrid approaches that many districts are considering for fall 2020, also typically include individualized content for students and seamless integration of online and classroom work.22 Educators also may want to consider using frequent formative assessments and focusing on active learning that includes robust discussion, collaborative work, video and audio clips and hands-on exercises when possible.23

Evidence review conclusions

The return to school presents enormous challenges to Pennsylvania’s education system, necessitating a balance between health and safety practices to reduce transmission and the potential learning losses from school closure and remote learning. Local education agencies, families, and educators should be aware that the virus presents relatively low risk to children, but schools might nonetheless be vectors of community transmission, posing larger risks to the adults with whom infected children come into contact. Evidence suggests that practices such as physical distancing, masking, ventilation, cleaning, and hygiene have the potential to mitigate the spread of COVID-19, including in school settings. These practices are further explored and illustrated in the stakeholder interview and agent-based modeling sections of the memo. Less evidence is available on the effectiveness of different approaches to remote and blended learning in education, but the evidence that does exist suggests the importance (and the challenge) of keeping students engaged when much of their learning must occur outside of school.


  1. Davies, N.G., Klepac, P., Liu, Y. et al. Age-dependent effects in the transmission and control of COVID-19 epidemics. Nat Med (2020).
  2. Munro, A. & Roland, D. (2020). The missing link? Children and transmission of SARS-CoV-2. Don't Forget the Bubbles.
  3. Dattner et al. (2020). The role of children in the spread of COBID-19: Using househol data from Bnei Brak, Israel, to estimate the relative susceptibility and infectivity of children. MedRxiv,
  4. CDC. (2020a, May 29). Caring for Children.
  5. CDC. (2020b, July 15) Health Department-Reported Cases of Multisystem Inflammatory Syndrome in Children (MIS-C) in the United States.
  6. CDC. (2020c, June 10) Provisional COVID-19 Death Counts by Sex, Age, and State.
  7. Staff, Toi (2020, May 30). Amid surge in Israel virus cases, schools in outbreak areas to be shuttered, The Times of Israel,
  8. Choon, Chang May (2020, May 13). South Korea races to contain new Covid-19 cluster linked to clubs as infections swell to 199. The Straits Times.
  9. Viner, R.M., Mytton, O.T., Bonell, C., Melendez-Torres, G.J., Ward, J.L., Hudson, L., Waddington, C., Thomas, J., Russell, S., van der Klis, F., Panovska-Griffiths, J., Davies, N.G., Booy, R., & Eggo, R. (2020). Susceptibility to and transmission of COVID-19 amongst children and adolescents compared with adults: a systematic review and meta-analysis. MedRXiv.
  10. Rauscher, Emily (2020) Lower State COVID-19 Deaths and Cases with Earlier School Closure in the U.S. MedRxiv.
  11. Chu et al. (2020). Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19:a systematic review and meta-analysis. The Lancet.
  12. Zhang, R., Li, Y., Zhang, A., Wang, Y., Molina, M. (2020) Identifying airborne transmission as the dominant route for the spread of COVID-19. Proceedings of the National Academy of Sciences.
  13. Somsen, G.A., van Rijn, C., Kooij, S., Bem, R., & Bonn, D. Small droplet aerosols in poorly ventilated spaces and SARS-CoV-2 transmission. The Lancet.
  14. Qian, H., Miao, T., Liu, L., Zheng, X. Luo, D., & Li, Y. (2020). “Indoor transmission of SARS-CoV-2.” MedRXiv. Available online at
  15. CDC. (2020d, July 24) Schools and Child Care Programs.
  16. Dorn, E., Hancock, B., and Sarakatsannis, J. (2020, June 1). COVID-19 and student learning in the United States: The hurt could last a lifetime. McKinsey & Company.
  17. Malkus, N. (2020, June 16). School districts’ remote learning plans may widen student achievement gap. Education Next.
  18. Petretto, D. R., Masala, I., & Masala, C. (2020). Special Educational Needs, Distance Learning, Inclusion and COVID-19.
  19. Heppen, J.B., Sorensen, N., Allensworth, E., Walters, K., Rickles, J., Stachel, S., \ Michelman, T., Michelman, V. (2017) The Struggle to Pass Algebra: Online vs. Face-to-Face Credit Recovery for At-Risk Urban Students, Journal of Research on Educational Effectiveness. DOI: 10.1080/19345747.2016.1168500
  20. Ahn, J. and McEachin, A. (2017) Student Enrollment Patterns and Achievement in Ohio’s Online Charter Schools. Educational Researcher.
  21. Hurwitz, F. & Malick, S. (2020). Instruction in the age of COVID-19: Exploring the evidence on remote learning. RELevant blog.
  22. Brodersen, R. M., & Melluzzo, D. (2017). Summary of Research on Online and Blended Learning Programs That Offer Differentiated Learning Options. Regional Educational Laboratory Central, REL 2017-228.
  23. California Department of Education (2020, March 17). Lessons from the Field: Remote Learning Guidance.