  Students develop and test simple kinetic models of the spread of COVID-19
caused by the novel SARS-CoV-2 virus. Microsoft Excel is used as the modeling
platform because it's non-threatening to students and because it's widely
available. Students develop simple finite difference models and implement them
in the cells of preformatted spreadsheets following a guided-inquiry pedagogy.
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
during April and May 2020 can be modeled using a Gaussian transition function
for the infection rate coefficient that can be easily implemented in Excel.
Answering similar active-learning questions, students discover that the summer
surge was caused by prematurely relaxing social distancing and then reimposing
stricter social distancing. By fitting published infection rate data up to
Thanksgiving (November 26, 2020), students discover that the beginning of the
fall surge can be explained by a return to more relaxed social distancing with
a similar infection rate constant as the inception of the summer surge.
Students then model the effect of vaccinations and validate the resulting SIR-V
model by showing that it successfully predicts the reported cases-per-day data
from November 26, 2020 through the holiday period up to February 20, 2021. The
success of the model in predicting the spread of COVID-19 during that time is a
remarkable validation of the SIR model and its SIR-V variant. See
http://circle4.com/biophysics for free sample textbook chapters and
instructional videos.
