Peter Hugo Nelson
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 this http URL for free sample textbook chapters and instructional videos.
Comments: 23 pages, 12 figures