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 © Copyright © 2020 Peker-Dobie, Demirci, Bilge and Ahmetolan
On the Time Shift Phenomena in Epidemic Models