On the Moments and the Distribution of the Cost of a Semi Markov Model for Healthcare Systems

In this paper we extend our previous semi-Markov reward model which attached costs to duration in states, by including costs of making a transition from one state to another. Theoretical results concerning the moments and consequently the distribution of interval costs for every member and of the total cost per unit period at any time and also through time intervals are obtained and provided in analytic form for the semi Markov reward model with discounting. The results are applied to an open healthcare system. In the healthcare domain such transition costs allow us to evaluate the overall costs of therapy or clinical intervention where an operation or other treatment may be an option. This model can be used for strategic approaches to planning and evaluating long-term patient care. The results demonstrate the potential of the model to demonstrate differential costs of different therapeutic strategies and explore optimal solutions.