Application of the chemical master equation and its analytical solution to the illness-death model

The aim of this article is relating the chemical master equation (CME) to the illness-death model for chronic diseases. We show that a recently developed differential equation for the prevalence directly follows from the CME. As an application, we use the theory of the CME in a simulation study about diabetes in Germany from a previous publication. We find a good agreement between the theory and the simulations.