Epidemiology and the SIR Model: Historical Context to Modern Applications

Abstract

We suggest the use of historical documents and primary sources, as well as data and articles from recent events, to teach students about mathematical epidemiology. We propose a project suitable -- in different versions -- as part of a class syllabus, as an undergraduate research project, and as an extra credit assignment. Throughout this project, students explore mathematical, historical, and sociological aspects of the SIR model and approach data analysis and interpretation. Based on their work, students form opinions on public health decisions and related consequences. Feedback from students has been encouraging. We begin our project by having students read excerpts of documents from the early 1900s discussing the Indian plague epidemic. We then guide students through the derivation of the SIR model by analyzing the seminal 1927 Kermack and McKendrick paper, which is based on data from the Indian epidemiological event they have studied. After understanding the historical importance of the SIR model, we consider its modern applications focusing on the Ebola outbreak of 2014-2016 in West Africa. Students fit SIR models to available compiled data sets. The subtleties in the data provide opportunities for students to consider the data and SIR model assumptions critically. Additionally, social attitudes of the outbreak are explored; in particular, local attitudes towards government health recommendations.

Mathematical Analysis of SIR Model for COVID-19 Transmission

“…Equation (2) indicates that, ( ) 0  dt t dS , i.e., in the elapse of time, the people in ( ) t S compartment will be decreased. ( ) t I initially increases exponentially, then moves to a plateau, and finally shrinks to zero if the disease is abolished completely after a finite time interval(Baez-Sanchez & Bobko, 2020;Bernardi & Aminian, 2021). At 0 = t the initial conditions of the model are(Murray, 2002),…”