Fig. 4: An example of a compartment model framework for IBD.

The compartment model for a chronic disease illustrates how individuals transition between three states: healthy, ill and deceased. These transitions are influenced by the individual’s age (a), disease duration (d) and calendar time (t). New cases of illness arise at the incidence rate (incidence (t,a)), whereas the recovery rate (recovery (t,a,d)) returns individuals from the ill to the healthy state. Two separate mortality rates are shown: mortality (t,a) for the healthy state and mortality (t,a,d) for the ill state, representing age-dependent and disease duration-dependent mortality (part A). The equation in part B captures this model mathematically, demonstrating how changes in age-specific prevalence over time (left) are influenced by the incidence rate, adjusted for the differential mortality between the general population and individuals with IBD, and accounting for migration from regions at different epidemiologic stages (right). Part C presents representative scenario analyses illustrating how incidence patterns affect the age structure of prevalence. A stable incidence rate from 2015 to 2045 (panel Ca) results in an upward and rightward shift of age-specific prevalence, with prevalence equilibrium occurring in the 2040s (panel Cc). By contrast, a scenario with slowly declining incidence (panel Cb) achieves a lower prevalence and an earlier transition to prevalence equilibrium (panel Cd). Representative data and model are based on methodology presented in refs. ^4,55. PDE, partial differential equation.