Overcrowded hospitals in its different process's levels is a very common issue all over the globe. Research through different works have studied this problem from different angles. Most of those focused on a very specific part of the internal flows. In this study, we present a mathematical model aiming to reflect patient flow and resources usage. This model presents a new perspective on how it is possible to organize a hospital flow for inpatients of different pathologies. It takes into consideration the patient's pathology, survival function and the current beds distribution and discharges. To model the different variations of a patient's flow, we used a non-homogenous discrete time Markov chain. Then, we tested our model using discrete event simulation using the National Health Service (NHS) dataset. The hospital episode statistics of the NHS used in this study included more than 12 million admission treated at NHS hospitals or care centers funded by the NHS in the period between March 2020 and February 2021. The results of the simulation model was then compared to the dataset using the chi-square goodness of fit test.
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