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The Susceptible-Infected-Recovered Model as a Tool to Motivate and Teach Differential Equations: An Analytic Approach

Authors :
Minchul Kang
Source :
International Journal of Mathematical Education in Science and Technology. 2024 55(2):273-294.
Publication Year :
2024

Abstract

Since the introduction by Kermack and McKendrick in 1927, the Susceptible-Infected-Recovered (SIR) epidemic model has been a foundational model to comprehend and predict the dynamics of infectious diseases. Almost for a century, the SIR model has been modified and extended to meet the needs of different characteristics of various infectious diseases including recent COVID-19 breakouts, which stimulates the advance in mathematical epidemiology theory significantly. Some of the mathematical ideas and techniques developed are also relevant to motivate teaching various topics in differential equations by connecting students' life experiences with current pandemics to meaningful classroom learning activities. Here, various pedagogically relevant topics from the SIR model are provided for undergraduate differential equation class, which includes (1) compartmental modelling and mass action kinetic modelling, (2) conservation rule and model reduction, (3) introduction to phase plane by removing time variable to derive trajectory equations, (4) transformation of equations to equivalent forms, (5) transformation of second-order system to second-order ODE, (6) deriving an analytic solution to the SIR equation by solving Bernoulli's equation, (7) deriving an analytic solution to the SIR equation from trajectory equations and (8) deriving an analytic solution to the SIR equation from exponential substitutions.

Details

Language :
English
ISSN :
0020-739X and 1464-5211
Volume :
55
Issue :
2
Database :
ERIC
Journal :
International Journal of Mathematical Education in Science and Technology
Publication Type :
Academic Journal
Accession number :
EJ1411101
Document Type :
Journal Articles<br />Reports - Research
Full Text :
https://doi.org/10.1080/0020739X.2023.2249898