We reproduced these spatio-temporal intermittency of turbulent puff split and decay based on the stochastic toy model of directed percolation (DP). Turbulent puffs form intermittently on a large scale at subcritical transitions in annular Couette flows (ACFs) with low radius ratios (r_in / r_out = 0.05-0.3) roughly like a pipe geometry. However, it is not generally the case that the splitting and decaying of puffs in an ACF coincide with that in a pipe flow, which is highly dependent on the difference in annular geometry, i.e., the radius ratio. Low-dimensional models have been proposed for the puffs of pipe flow in terms of dynamical systems and DP universality, but for ACF we adopted the Domany-Kinzel model, which extends the DP to two stochastic variables. It was possible to exhaustively reproduce a fractal-like STI for low radius ratios to mean-field-like structures for medium radius ratios by controlling the frequency of puff advection (splitting) and coalescence with the two variables of the Domany-Kinzel model, respectively.