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ODE Model, COVID-19 Pandemic, Parameter Estimation


Epidemiology | Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education


In May 2020, administrators of residential colleges struggled with the decision of whether or not to open their campuses in the Fall semester of 2020. To help guide this decision, we formulated an ODE model capturing the dynamics of the spread of COVID-19 on a residential campus. In order to provide as much information as possible for administrators, the model accounts for the different behaviors, susceptibility, and risks in the various sub-populations that make up the campus community. In particular, we start with a traditional SEIR model and add compartments representing relevant variables, such as quarantine compartments and a hospitalized compartment. We then duplicated the model for ten interacting sub-populations, resulting in a large system of differential equations. The model predicts possible outcomes based on hypothetical administrative policies such as masking, social distancing, and quarantining. As the pandemic developed, we updated the model to account for new policies, such as testing and vaccination and calibrated the model to data gathered from local sources. To complete the modeling process, we describe the parameter-fitting procedure, in which we used publicly available data from the county, as well as specific descriptions of our student body, faculty, and staff. The final stage of the work involved performing numerical simulations and designing an interactive application that allows non-mathematicians to experiment with a range of scenarios. We then extrapolate the findings of our model to a general audience, which along with our plots and app makes model conclusions accessible to all, democratizing the policy-making process.



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