Using Markov Models to Manage High Occupancy Hospital Care

We have previously used Markov models to describe movements of patients between hospital states; these may be actual or virtual and described by a phase-type distribution. Here we extend this approach to a Markov reward model for a healthcare system with constant size. This corresponds to a situation where there is a waiting list of patients so that the total number of in-patients remains at a constant level and all admissions are from the waiting list. The distribution of costs is evaluated for any time and expressions derived for the mean cost The approach is then illustrated by determining average cost at any time for a hospital system with two states: acute/rehabilitative and long-stay. In addition, we develop a Markov model to determine patient numbers and costs at any time where, again, there is a waiting list, so admissions are taken from this list, but we now allow a fixed growth which declines to zero as time tends to infinity. As before, the length of stay is described by a phase-type distribution, thus enabling the representation of durations and costs in each phase within a Markov framework. As an illustration, the model is used to determine costs over time for a four phase model, previously fitted to data for geriatric patients. Such an approach can be used to determine the number of patients and costs in each phase of hospital care thus facilitating an intelligent and systematic approach to the planning of healthcare and optimal use of scarce resources