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We study the relation between the age-specific prevalence, incidence andmortality in an illness-death model consisting of the three states Healthy,Ill, Dead. The dependency on three different time scales (age, calendar time,disease duration) is considered. It is shown that Keiding's equation publishedin 1991 is a generalisation of the solution of Brunet and Struchiner's partialdifferential equation from 1999. In a special case, we propose a particularlysimple estimate of the incidence from prevalence data.

On Keiding's Equation and its relation to differential equations about prevalence and incidence in chronic disease epidemiology