Emphasizing Visual Tools: Using R to Understand Dynamic Models of Biology and Epidemiology

Epidemiological models have enhanced relevance because of the COVID-19 pandemic. In this note, we emphasize visual tools that can be part of a learning module geared to teaching the SIR epidemiological model, suitable for advanced undergraduates or beginning graduate students in disciplines where the level of prior mathematical knowledge of students may not be very strong. Visual tools -- phase portrait, flow field and trajectory and line plots -- available in the R software are presented in a step by step manner, moving from the exponential growth model to the logistic growth model and then to the SIR model. Code for numerical simulation of differential equations and estimation of parameters is presented for the SIR model. Suggestions for students to connect the learning from these examples with research papers on COVID-19 are provided.