Compartmental models for which transfer from one compartment to another takes a non-negligible time have been studied in the deterministic case. These models rely on the use of differential equations with delayed arguments. In this paper we show how the well-known structure of the semi-Markov process can be used to analyse stochastic compartmental models with transfer delays. Evaluation of the limiting behavior is much simpler in the stochastic model than in previous deterministic formulations. In addition, time-dependent behavior can be analysed using numerical quadrature methods.
