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A Mathematical Model of Epidemics—A Tutorial for Students

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yutaka Okabe & Akira Shudo, 2020. "A Mathematical Model of Epidemics—A Tutorial for Students," Mathematics, MDPI, vol. 8(7), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1174-:d:385867
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    References listed on IDEAS

    as
    1. James H. Stock, 2020. "Data Gaps and the Policy Response to the Novel Coronavirus," NBER Working Papers 26902, National Bureau of Economic Research, Inc.
    2. Fernández-Villaverde, Jesús & Jones, Charles I., 2022. "Estimating and simulating a SIRD Model of COVID-19 for many countries, states, and cities," Journal of Economic Dynamics and Control, Elsevier, vol. 140(C).
    3. Dimitrios E. Panayotounakos & Theodoros I. Zarmpoutis, 2011. "Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations)," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-13, October.
    4. Andrew Atkeson, 2020. "What Will be the Economic Impact of COVID-19 in the US? Rough Estimates of Disease Scenarios," Staff Report 595, Federal Reserve Bank of Minneapolis.
    Full references (including those not matched with items on IDEAS)

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