A compartmental model to describe acute medical in-patient flow through a hospital

Managing patient flow in hospitals is a critical part of effective secondary care. Considering a hospital as a multi-compartment system through which patients pass, we will derive relevant equations to allow a description of patient flow through these departments as a series of interconnected dynamic relationships. These relationships are determined by many factors, some known, and many interdependent. We do not need to, and indeed cannot, know all of these factors (as needed for discrete event simulation, or agent-based modelling), but will merely examine the net changes between compartments (i.e. a 'system dynamics' approach). Using this approach, we were able to identify two relevant states of equilibrium: the first (trivial) is when the hospital is empty; the second, is when there is activity. We plan to use bed usage data from a UK hospital in an attempt to validate this methodology and then assess its generalizability.