The discrete-time Kermack-McKendrick model: A versatile and computationally attractive framework for modeling epidemics

Odo Diekmann, Hans G. Othmer, Robert Planqué*, Martin C.J. Bootsma

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

The COVID-19 pandemic has led to numerous mathematical models for the spread of infection, the majority of which are large compartmental models that implicitly constrain the generation-time distribution. On the other hand, the continuoustime Kermack-McKendrick epidemic model of 1927 (KM27) allows an arbitrary generation-time distribution, but it suffers from the drawback that its numerical implementation is rather cumbersome. Here, we introduce a discrete-time version of KM27 that is as general and flexible, and yet is very easy to implement computationally. Thus, it promises to become a very powerful tool for exploring control scenarios for specific infectious diseases such as COVID-19. To demonstrate this potential, we investigate numerically how the incidence-peak size depends on model ingredients. We find that, with the same reproduction number and the same initial growth rate, compartmental models systematically predict lower peak sizes than models in which the latent and the infectious period have fixed duration.

Original languageEnglish
Article numbere2106332118
Pages (from-to)1-9
Number of pages9
JournalProceedings of the National Academy of Sciences of the United States of America
Volume118
Issue number39
DOIs
Publication statusPublished - 28 Sep 2021

Bibliographical note

Publisher Copyright:
© 2021 National Academy of Sciences. All rights reserved.

Keywords

  • Basic reproduction number
  • Discrete-time model
  • Epidemic outbreak
  • Incidence peak
  • Kermack-McKendrick

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