Geriatric-patient flow-rate modelling

Abstract

We consider the application of a three-compartment mathematical model using difference equations in discrete time to model the flow of patients through departments of geriatric medicine. It has been shown empirically that the time spent in hospital since admission may be described by a two-term mixed-exponential distribution. Previous work has explained this empirical finding in terms of a two-compartment model of geriatric in-patient behaviour where the two compartments are acute/rehabilitative and long-stay care. Our model extends this approach by considering patients released from geriatric departments and their subsequent length of stay in the community. We have therefore, two states of patient behaviour while in hospital: (i) patients can be admitted to the acute-rehabilitative state, from which they may die or be released back into the community; (ii) patients can be admitted to the long-stay state, from which they eventually die. The community state currently has only one state, from which patients may be readmitted back into the geriatric department or they may die. The model may then be used to estimate the average numbers and lengths of stay for short-term and long-term patients and the average number and length of stay in the community for released patients, allowing for a significant improvement in the forecasting of future bed requirements to aid the planning of geriatric departments.