Conclusions from an integral equation about the prevalence-odds in the illness-death model for chronic diseases

This research note explores the mathematical structure of the prevalence-odds integral equation for chronic disease dynamics recently formulated by Saem and Brinks (2024). We provide a rigorous derivation of the Brunet- Struchiner partial differential equation from the integral representation under duration-independent mortality. Furthermore, we examine the strict limiting conditions under which the integral collapses into the classical epidemiological heuristic that prevalence-odds is the product of incidence and disease duration.