On the Time Shift Phenomena in Epidemic Models

On the Time Shift Phenomena in Epidemic Models

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

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 R′(t) and the peak of J(t)=∑iIi(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 Ii is 1/γi, where 1/γi is the infectious period of the ith infectious stage, and we present numerical calculations that confirm this approximation.

2020

covid-19, epidemic models, time shift, multistage Susceptible-Infected-Removed model, multistage Susceptible-Exposed-Infected-Removed model

10.3389/fphy.2020.578455

Epidemiology and Health

Korean Society of Epidemiology

Physics