A Mathematical Model of Epidemics—A Tutorial for Students

Yutaka Okabe and Akira Shudo
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Yutaka Okabe: Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
Akira Shudo: Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan

Mathematics, 2020, vol. 8, issue 7, 1-16

Abstract: This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.

Keywords: SIR model; numerical solution; exact solution; Bernoulli differential equation; Abel differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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