Using a continuous-time Markov model with Poisson arrivals to describe the movements of geriatric patients

The population of geriatrics in a given hospital district is relatively stable and therefore we may model the movement on geriatric patients by considering both their stays in hospital and subsequent releases back into the community. The care of the elderly in departments of geriatric medicine may be generally classified into two forms of clinical care, acute/rehabilitative and long stay. Our paper describes the movement of patients through departments of geriatric medicine and subsequent stays in the community by a four-stage continuous-time Markov model. The stages represent acute/rehabilitative patients, long-stay patients, ex-patients in the community and former patients who are now dead, respectively. Admissions are modelled as a Poisson stream and expressions are calculated for the distribution, mean and variance of numbers of patients in each compartment at any time. Using these expressions the model is then fitted to a large data set of hospital spells containing over 10000 admissions.