Hi Say a company used a a time-homogenous model to model Healthy - Sick transitions of its employees and subsequently found that the mean holding times (say in sick state) increases with time. Explain why the time-homogeneous model could still be used if the company have large and constant employees' age profiles.
Not sure what you mean... If you mean "...increase with age" instead of time, then as long as the population is stable, I don't see why you shouldn't be able to use a time-homogeneous model, since you would be able to set transition rates to be averages depending on the age profile of the population. If on the other hand you mean that the longer someone is sick, the lower their recovery rate (i.e. duration dependence), then I think a time-inhomogeneous model is required: see pages 27-29 of chapter 6 of the ActEd notes.
