Age- and time-dependent model of the prevalence of non-communicable diseases and application to dementia in Germany

We derive a partial differential equation (PDE) that models the age-specific prevalence of a disease as a function of the incidence, remission and mortality rates. The main focus is on non-communicable diseases (NCDs), although the PDE is not restricted to NCDs. As an application of the PDE, the number of persons with dementia in Germany until the year 2050 is estimated based on German incidence data and official population projections. Uncertainty is treated by different scenarios about life expectancy, number of migrants, prevalence of the disease in migrants, and scenarios about the future incidence, and mortality of demented persons. Life expectancy and incidence of dementia have the strongest impact on the future number of persons with dementia. In nearly all scenarios, our estimated case numbers exceed former estimates. Furthermore, we use an example to show that the PDE method yields more accurate results than a common alternative approach.