The authors propose a continuous-time Markov model for description of the movements of a cohort of patients entering the system at time \(t=0\). Patients are initially admitted into acute care \((S_{1})\), from where they may: (1) be released and therefore reenter the community of released patients \((S_{3})\); (2) die \((S_{4})\); or (3) they may be considered to be unable to look after themselves and therefor be moved into long-stay care \((S_{2})\) where they will eventually die \((S_{4})\). Patients who have been released back into the community \((S_{3})\) may be readmitted to acute care \((S_{1})\) or die \((S_{4})\).
The authors obtain the transition probability matrix and calculate the expected number of patients in a state \((S_{i}),\;i=1,\ldots,4\), and variances of these numbers. This model is fitted to data from St George’s Hospital, London, using the method of maximum likelihood.