Introductory Models of COVID-19 in the United States

Abstract

Students develop and test simple kinetic models of the spread of coronavirus disease 2019 (COVID-19) caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Microsoft Excel is used as the modeling platform because it is nonthreatening to students and it is widely available. Students develop finite difference models and implement them in the cells of preformatted spreadsheets following a guided inquiry pedagogy that introduces new model parameters in a scaffolded step-by-step manner. That approach allows students to investigate the implications of new model parameters in a systematic way. Students fit the resulting models to reported cases per day data for the United States using least squares techniques with Excel's Solver. Using their own spreadsheets, students discover for themselves that the initial exponential growth of COVID-19 can be explained by a simplified unlimited growth model and by the susceptible-infected-recovered (SIR) model. They also discover that the effects of social distancing can be modeled using a Gaussian transition function for the infection rate coefficient and that the summer surge was caused by prematurely relaxing social distancing and then reimposing stricter social distancing. Students then model the effect of vaccinations and validate the resulting susceptible-infected-recovered-vaccinated (SIRV) model by showing that it successfully predicts the reported cases per day data from Thanksgiving through the holiday period up to 14 February 2021. The same SIRV model is then extended and successfully fits the fourth peak up to 1 June 2021, caused by further relaxation of social distancing measures. Finally, students extend the model up to the present day (27 August 2021) and successfully account for the appearance of the delta variant of the SARS-CoV-2 virus. The fitted model also predicts that the delta variant peak will be comparatively short, and the cases per day data should begin to fall off in early September 2021, counter to current expectations. This case study makes an excellent capstone experience for students interested in scientific modeling.