AUTHOR=Peker-Dobie Ayse , Demirci Ali , Bilge Ayse Humeyra , Ahmetolan Semra 

TITLE=On the Time Shift Phenomena in Epidemic Models

JOURNAL=Frontiers in Physics

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.578455

DOI=10.3389/fphy.2020.578455

ISSN=2296-424X

ABSTRACT=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 \citep{bib19}  displayed  a time shift  between the hospital referrals and fatalities. An analysis of recent  Covid-19 data \citep{ahmetolan2020can} and the records for Spanish flu (1918-1919) and SARS (2002-2004) epidemics confirm this observation. We use multistage $SIR$ and $SEIR$ models \citep{bib14}  to provide an explanation for this  time shift. Numerical solutions of these models present strong evidence that the delay between the peak of $R'(t)$  and the peak of  $J(t)=\sum_i I_i(t)$ 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  $I_i$  is $1/\gamma_{i}$ where $1/\gamma_{i}$ is the infectious period of the $i$th infectious stage  and we present  numerical calculations that confirm this approximation.