Stochastic models for geriatric in-patient behaviour.

Departments of geriatric medicine engage in two distinct forms of clinical activity: acute/rehabilitative and long-stay care. These are organizationally distinct and have very different resource needs. Current hospital planning models, however, assume that patients all move through the system at the same rate, thereby ignoring this effect of inherent heterogeneity in patient behaviour. The present paper describes the movement of patients through geriatric hospitals by a two-stage continuous-time Markov model, where the stages represent acute/rehabilitative and long-stay patients respectively. Patients are initially admitted to the first stage, from which they may depart from the system, by death or discharge, or move into the second stage, from which they eventually depart by death or discharge (unlikely). Admissions are modelled in two ways: either as replacements for departures or as a Poisson stream. Expressions for the distribution and movement of numbers of patients are derived and evaluated for data from a number of hospitals. Such an approach has the advantage, over previous crude models, of taking into account different types of patients and introducing variability, thus making it possible to extract variances as well as means of numbers of geriatric patients requiring hospital care.