About the model

This model was developed is model was developed in collaboration with Carl Bergstrom and Ryan McGee from the University of Washington. It can be used to simulate infection dynamics of SARS-CoV-2 and evaluate the impact different mitigation strategies have on outbreaks in primary and secondary schools. This model is used in our pre-print “Model-driven mitigation measures for reopening schools during the COVID-19 pandemic”.

For a detailed description of the model and methods, please refer to our pre-print and supplementary material:

• Model-driven mitigation measures for reopening schools during the COVID-19 pandemic
• Supplementary Material

SEIRS+ model

This interactive modeling tool uses a modified version of the SEIRS+ model, which was developed by Ryan McGee, Carl Bergstrom, and colleagues at the University of Washington.

SEIR models are epidemiological models that are used to model the spread of disease in a population. Standard SEIR models are compartmental models, meaning they track the proportion of the population in different disease states over time. SEIR models include compartments for susceptible (S), exposed (E), infectious (I), and recovered (R) disease states.

The SEIRS+ model is an extended SEIR model, which incorporates the effects of stochastic dynamics, network structure, SARS-CoV-2 testing, and additional interventions in a population.

Further information and code for the SEIRS+ model framework can be found at:

• https://github.com/ryansmcgee/seirsplus

Primary versus secondary schools

The dynamics of SARS-CoV-2 transmission differ substantially between primary schools and secondary schools for two principal reasons: (1) children (under age 10) and adolescents (ages 10-19) appear to have different epidemiological characteristics of infection, and (2) primary and secondary schools have different organizational structures.

Primary schools are often structured into more stable cohorts, with groups of students assigned to a single teacher for their entire day. In contrast, secondary school students typically move from classroom to classroom and thus encounter multiple teachers and groups of students over the course of a single day.

For these reasons, we have developed two distinct models for primary versus secondary schools, each with parameters chosen to reflect these critical differences.

Model network structure

The contact structures of schools differ from other settings. For our primary school model, we simulate a medium-sized school of 480 students with 24 teachers and 24 additional staff (Table 2). Each class comprises one teacher and 20 students that interact with one another. Additionally, each teacher interacts with a handful of other teachers and staff, and students that share the same household (as calibrated by United States (US) census data) are connected. Most of the contacts that an individual makes in the school population are with the students and teacher in their own class, and disease transmission within a class is more likely than between classes.

For our secondary school model, we consider both (a) a medium-sized school with 800 students (200 per graduating class), 125 teachers, and 75 staff and (b) a large school with 2,000 students (500 per graduating class), 175 teachers, and 75 staff (Table 3). We define network layers for students, teachers, and staff using the FARZ network generation algorithm, which allows us to calibrate epidemiologically-important network properties (e.g., community structure, assortativity, clustering coefficient) to values consistent with studies of secondary school contact networks. A FARZ community network layer is generated for each grade, with students belonging to one or more communities of about 10 individuals. 80% of each student’s contacts are with students in the same grade, and 80% of those within-grade contacts are with students in their own communities. Students that share a household (as calibrated by US census data) are connected as well. Interactions between teachers and staff are represented by another FARZ network layer with a total of six communities. Finally, students are connected with six random teachers with whom they have classes, with students in the same grade being more likely to share teachers.

Model parameters

The parameter values and descriptions used in the model are listed in the table below.

Table 1. Table of parameters included in model

Table 2. Model assumptions for primary schools

Table 3. Model assumptions for secondary schools

Limitations

Modeling can be extremely important to help us understand epidemic progression, however, all models have assumptions, limitations, and biases that make them imperfect estimates. While we do our best to pick the most accurate and evidence-based parameters about SARS-CoV-2 disease spread, estimates for these parameters vary and may change as we learn more about the SARS-CoV-2 virus. Because these parameter choices can have significant impacts on model outcomes, we cannot guarantee our choices are always correct, and any results produced by this model should not be interpreted to predict exact numbers of cases or outcomes.

We describe the limitations of our model in further detail in our pre-print.

References