On the Time Shift Phenomena in Epidemic Models - Peker-Dobie, Ayse; Demirci, Ali; Bilge, Ayse Humeyra; Ahmetolan, Semra (Frontiers in Physics, 2020)
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 bib19 displayed a time shift between the hospital referrals and fatalities. An analysis of recent Covid-19 data ahmetolan2020can and the records for Spanish flu (1918-1919) and SARS (2002-2004) epidemics confirm this observation. We use multistage SIR and SEIR models 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)=_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/γ_i where 1/γ_i is the infectious period of the ith infectious stage and we present numerical calculations that confirm this approximation.