Introductory models of COVID-19 in the United States

Nelson, Peter Hugo

Students develop and test simple models of the spread of COVID-19. Microsoft Excel is used as the modeling platform because it's non-threatening to students and because it's 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 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 SIRV model by showing that it successfully predicts the reported cases-per-day data from Thanksgiving through February 14, 2021. The same SIRV model is then extended and successfully fits the fourth peak up to June 1, 2021, caused by further relaxation of social distancing measures. Finally, students extend the model up to the present day and successfully account for the appearance of the delta variant of SARS-CoV-2. 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 would make an excellent capstone experience for students interested in scientific modeling.