Fig. 3.

Example diagram of transitions out of a given state (X) and into multiple states (Y${}_1$ and Y${}_2$). Different assumptions about (1) the dwell times in X, and (2) rules governing the subsequent transitions to Y${}_1$ and/or Y${}_2$ will lead to different sub-state partitions of X, and thus different mean field equations, as detailed in Sect. 3.5. Fortunately, different scenarios often encountered in applications can be reduced to ODEs by applying the results in Sect. 3.5 as detailed in Theorems 4, 5, and 6 and as illustrated in Figs. 4, 5, and 6