On the Time Shift Phenomena in Epidemic Models

Ayse Peker-Dobie, Ali Demirci*, Ayse Humeyra Bilge, Semra Ahmetolan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In the standard Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models, the peak of infected individuals coincides with the inflection point of removed individuals. Nevertheless, a survey based on the data of the 2009 H1N1 epidemic in Istanbul, Turkey displayed a time shift between the hospital referrals and fatalities. An analysis of recent COVID-19 data and the records for Spanish flu (1918–1919) and SARS (2002–2004) epidemics confirm this observation. We use multistage SIR and SEIR models to provide an explanation for this time shift. Numerical solutions of these models present strong evidence that the delay between the peak of (Formula presented.) and the peak of (Formula presented.) is approximately half of the infectious period of the epidemic disease. In addition, we use a quadratic approximation to show that the distance between successive peaks of (Formula presented.) is (Formula presented.), where (Formula presented.) is the infectious period of the ith infectious stage, and we present numerical calculations that confirm this approximation.

Original languageEnglish
Article number578455
JournalFrontiers in Physics
Publication statusPublished - 18 Nov 2020

Bibliographical note

Publisher Copyright:
© Copyright © 2020 Peker-Dobie, Demirci, Bilge and Ahmetolan.


  • COVID-19
  • epidemic models
  • multistage Susceptible-Exposed-Infected-Removed model
  • multistage Susceptible-Infected-Removed model
  • time shift


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