  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.
