Modeling the temporal prevalence peak drift of chronic diseases

Chronic diseases, such as type 2 diabetes, are responsible for a substantial proportion of global deaths and are marked by an increasing number of people that suffer from them. Our objective is to systematically investigate the analytical determination of the drift in prevalence peaks over calendar-time and age, with an emphasis on understanding the intrinsic attributes of temporal displacement. This aims to enhance the understanding of disease dynamics that may contribute to refining medical strategies and to plan future healthcare activities.

We present two distinct yet complementary approaches for identifying and estimating drifts in prevalence peaks. First, assuming incidence and mortality rates are known, we employ a partial differential equation that relates prevalence, incidence, and mortality. From this, we derive an ordinary differential equation to mathematically describe the prevalence peak drift. Second, assuming prevalence data (rather than incidence and mortality data) are available, we establish a logistic function approach to estimate the prevalence peak drift. We applied this method to data on the prevalence of type 2 diabetes in Germany.

The first approach provides an exact mathematical prescription of the trajectory of the prevalence peak drift over time and age, assuming incidence and mortality rates are known. In contrast, the second approach, a practical application based on available prevalence data, demonstrates the prevalence peak dynamics in a real-world scenario. The theoretical model, together with the practical application, effectively substantiates the understanding of prevalence peak dynamics in two different scenarios.

Our study shows the theoretical derivation and determination of prevalence peak drifts. Our findings underpin the dynamic nature of chronic disease prevalence, highlighting the importance of considering the related age-dependent trends for planning future healthcare activities.