Approximation of the infection-age-structured SIR model by the conventional SIR model of infectious disease
1Medical Biometry and Epidemiology, Faculty of Health/School of Medicine, Witten/Herdecke University, Witten, Germany.
Abstract:
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.
Related Concept Videos
Steps in Outbreak Investigation
Stages of Infection
Parametric Survival Analysis: Weibull and Exponential Methods
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Survival Curves
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...
Factors Affecting the Risk of Infection
The integrity and count of the white blood cells help the body resist pathogens and fight infection. When impaired, it reduces the body's resistance to pathogens. The acidic pH levels of the gastrointestinal, genitourinary tracts, and skin...
Actuarial Approach
Consider the example of a high-risk surgical procedure with significant early-stage mortality. A two-year clinical study is conducted,...


