Approximation of the infection-age-structured SIR model by the conventional SIR model of infectious disease epidemiology.

During the SARS-CoV-2 pandemic, the effective reproduction number (R-eff) has frequently been used to describe the course of the pandemic. Analytical properties of R-eff are rarely studied. We analytically examine how and under which conditions the conventional susceptible-infected-removed (SIR) model (without infection age) serves as an approximation to the infection-age-structured SIR model. Special emphasis is given to the role of R-eff, which is an implicit parameter in the infection-age-structured SIR model and an explicit parameter in the approximation. The analytical findings are illustrated by a simulation study about an hypothetical intervention during a SARS-CoV-2 outbreak and by historical data from an influenza outbreak in Prussian army camps in the region of Arnsberg (Germany), 1918-1919.