Modelling capacity along a patient pathway with delays to transfer and discharge

This article presents a versatile model to estimate capacity requirements along a patient pathway with delays to transfer and discharge caused by blocking after service. Blocking after service is a common property in health systems where patients requiring uninterrupted care can only leave a service when they can be admitted downstream to another. Unlike many studies, the approach appreciates both variability in arrivals and length of stay at each service point and the stochastic queuing dynamics between them. This is crucial to the understanding and identification of blockages which can present a significant source of inefficiency. The problem is framed as a continuous-time Markov chain where patient arrivals, transfers, and discharges are modelled through state transitions, with length of stay approximated by the Erlang distribution. The solution is through simulating movements around this chain by dynamically sampling the next state accessible from the neighbourhood of the current, thus bypassing the need for time-intensive manipulations of equations involving the entire transition matrix. This is packaged in easy-to-use code in free software so as to be readily available to healthcare practitioners. An example of use is illustrated for a stroke pathway reconfiguration where move to a centralised hyper-acute service is assessed.