Markovian Approach for Analyzing Patient Flow Data: A Study of Kapsabet County Referral Hospital, Kenya

Abstract

Hospital is indispensable and necessary welfare of society. Through it, we can manage our illnesses by treatment and prevention interventions. With the rise incidences of chronic diseases and illnesses, there has been an increased demand for health care services round the world. This demand has subsequently caused a serious pressure resulting to serious episodes of congestion and overcrowding in hospitals. Hospital overcrowding and congestion, has always been a problem to patients, hospital administration and to the general health workers. Hospitals are struggling to alleviate congestion and overcrowding. In this study, we developed an objective patient flow estimation using Markov chain models. Weekly data from Kapsabet County Referral Hospital facility was used to assess the flow. Markov chains’ transition probability matrices were constructed for each day in a week. Markov chain’s four-state model used was; High, Medium, Low and Very Low. The future n step transition probabilities matrices were computed, giving rise to steady state for each day of the week. It was examined that the patient flow had some pattern through the Markov chains’ steady states. The steady state probability of the flow is high on Mondays with highest probability of 0.57. Medium on Tuesdays through to Thursdays with steady state probabilities ranging from 0.36 and 0.3 respectively. On Fridays the probabilities decrease from 0.22 to 0.12 on Sunday. Through this study, we can witness some pattern from steady state of transition matrices. This way, the patient’s population flow throughout the week at this facility is identified. Generally, through this study, the patient flow is understood and hence the patient flow congestion can be easily attenuated.