One of the biggest challenges that hospital management teams face is the uncertainty of when patients will be admitted to and discharged from hospital. Due to the limited capacity of hospital resources this imposes a substantial stress on staff, having to spend a significant amount of time each day planning for bed availability. Therefore, the development of a mathematical model able to predict discharge times of patients would save a substantial amount of time and resources to hospitals.
Some of the factors affecting discharge times of patients are unpredictable, such as capacity in care homes and transport facilities for patients with social care needs. Therefore, we propose to develop a mathematical model that describes the inherent stochasticity of the process that governs patient flow through a hospital. By modifying a model we previously developed describing traffic of ribosomes along messenger RNAs, we will be able to describe the flow of patients through the different hospital stations or wards. Treating patients as individual stochastic particles moving through a network representing the different units or wards within the hospital, this model will facilitate the prediction discharge times of patients. Importantly, the model will also help determine bottlenecks in the hospital network, thereby suggesting improvements in the hospital structure design to optimise patient flow.