  The illness-death model of a chronic disease consists of the states 'Normal',
'Disease' and 'Death'. In general, the transition rates between the states
depend on three time scales: calendar time, age and duration of the chronic
disease. Previous works have shown that the age-specific prevalence of the
chronic disease can be described by differential equations if the duration is
negligible. This article derives a partial differential equation (PDE) in the
presence of duration dependency. As an important application, the PDE allows
the calculation of the age-specific incidence from cross-sectional surveys.
