A modeling framework that combines Markov models and discrete-event simulation for stroke patient care

Stroke disease places a heavy burden on society, incurring long periods of hospital and community care. Also stroke is a highly complex disease with heterogeneous outcomes and multiple strategies for therapy and care. In this article we develop a modeling framework that clusters patients with respect to their length of stay (LOS); phase-type models are then used to describe patient flows for each cluster. In most cases, there are multiple outcomes, such as discharge to normal residence, nursing home, or death. We therefore derive a novel analytical model for the distribution of LOS in such situations. A model of the whole care system is developed, based on Poisson admissions to hospital, and results obtained for expected numbers in different states of the system at any time. We can thus describe the whole integrated system of stroke patient care, which will facilitate planning of services. We also use the basic model to build a discrete-event simulation, which incorporates back-up queues to model delayed discharge. Based on stroke patients' data from the Belfast City Hospital, various scenarios are explored with a focus on the potential efficiency gains if LOS, prior to discharge to a private nursing home, can be reduced. Predictions for bed occupancy are also provided. The overall modeling framework characterizes the behavior of stroke patient populations, with a focus on integrated system-wide planning, encompassing hospital and community services. Within this general framework we can develop either analytic or simulation models that take account of patient heterogeneity and multiple care options.