Modeling Hospital Patient Flow as an Interconnected Compartmental System: Equilibrium and Stability Analysis

Efficiently directing patient movement within hospitals is essential for delivering effective secondary care. By treating a hospital as a set of linked compartments through which patients transition, we formulate equations that describe these flows as a network of interdependent dynamic processes. Many influences shape these interactions—some identifiable, many interacting in complex ways. Unlike discrete-event or agent-based methods, this approach does not require detailed knowledge of every underlying factor; instead, it focuses on the overall transfers between units, consistent with a system-dynamics framework. Using this perspective, we identify two equilibrium conditions: a trivial state in which no patients are present, and a non-trivial state representing ongoing activity. We intend to analyse bed-occupancy data from a UK hospital to test the validity of this approach and evaluate how widely it can be applied.