Introduction: Estimates of future disease burden supports public health decision-making. Multistate modeling of chronic diseases is still limited despite a long history of mathematical modeling of diseases. We introduce a discrete time approach to the illness-death model and a recursion formula, which can be utilized to project chronic disease burden. We further illustrate an example of the technique applied to anxiety disorders in Germany.

Materials and Equipment: The illness-death model is a multistate model that relates prevalence, incidence, mortality, and remission. A basic recursion formula that considers prevalence, incidence, mortality among the susceptible, and mortality among the diseased can be applied to irreversible chronic diseases such as diabetes. Among several mental disorders, remission plays a key role and thus an extended recursion formula taking remission into account is derived.

Methods: Using the Global Burden of Disease Study 2019 data and population projections from the Federal Statistical Office of Germany, a total number of individuals with anxiety disorders by sex in Germany from 2019 to 2030 was projected. Regression models were fitted to historical data for prevalence and incidence. Differential mortality risks were modeled based on empirical evidence. Remission was estimated from prevalence, incidence, and mortality, applying the extended recursion formula. Sex- and age-specific prevalence of 2019 was given as the initial value to estimate the total number of individuals with anxiety disorders for each year up to 2030. Projections were also made through simple extrapolation of prevalence for comparison.

Results: From 2019 to 2030, we estimated a decrease of 52,114 (−1.3%) individuals with anxiety disorders among women, and an increase of 166,870 (+8.5%) cases among men, through the illness-death model approach. With prevalence extrapolation, an increase of 381,770 (+9.7%) among women and an increase of 272,446 (+13.9%) among men were estimated.

Discussion: Application of the illness-death model with discrete time steps is possible for both irreversible chronic diseases and diseases with possible remissions, such as anxiety disorders. The technique provides a framework for disease burden prediction. The example provided here can form a basis for running simulations under varying transition probabilities.