A mathematical model of an integrated haemodialysis and renal transplantation programme.

A mathematical model of an integrated renal dialysis and transplantation programme is described. The three treatment areas—hospital dialysis, home dialysis, and transplantation—are represented in the model by three states and those states are subdivided into one and two substates respectively. Interstate transitions occur at either constant average rate or with constant average probability, depending on the relevant principal constraints. In estimating future numbers in the programme, interstate transition probabilities (or rates) may be adjusted for possible changes, such as an improvement in graft survival. Projection based on data of the early years of the Cardiff unit are compared with developments in later years. The model may be used for the calculation of future numbers in other centres or nationally by substituting the appropriate interstate transition probabilities or rates.