Discrete semi Markov patient pathways through hospital care via Markov modelling

Abstract

In the present paper, we study the movement of patients through hospital care where each patient spends an amount of time in hospital, referred to as length of stay (LOS). In terms of semi-Markov modelling we can regard each patient pathway as a state of the semi-Markov model, therefore the holding time distribution of the ith state of the semi-Markov process is equivalent to the LOS distribution for the corresponding patient pathway. By assuming a closed system we envisage a situation where the hospital system is running at capacity, so any discharges are immediately replaced by new admissions to hospital. In the present paper a method is applied according to which we can describe first and second moments of numbers in each semi Markov patient pathway at any time via Markov modelling. Such values are useful for future capacity planning of patient demand on stretched hospital resources. The above results are illustrated numerically with healthcare data.