Emphasizing visual tools: using R to understand dynamic models of biology and epidemiology

ABSTRACT

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.

Keywords:

• COVID-19
• differential equations
• exponential growth
• logistic growth
• SIR model
• R software

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 34-01

Disclosure statement

No potential conflict of interest was reported by the author.

Data availability statement

The paper uses three datasets. Two datasets are openly available in packages (Bjornstad, 2020; Clark et al., 2020) in the open access software R (R Core Team, 2020), which can be freely downloaded. One dataset (Ritchie et al., 2020) is openly available in https://github.com/owid/covid-19-data/tree/master/public/data, is continuously updated, and was accessed by the author on 9 May 2021.