A model for molecular-beam epitaxial growth on a vicinal surface that takes into account the step advance, nucleation and growth of islands on a terrace and possible existence of repulsive Ehrlich-Schwoebel (ES) barrier at a descending step edge is further refined and compared with experiments on the GaAs(1 0 0) homoepitaxy performed with in situ reflection high-energy electron diffraction monitoring of a growing layer surface morphology. On the basis of model calculations with simple criteria for growth mode transitions, the phase diagram of the growth mode in 2D space of parameters, characterizing the adatom surface diffusion rate and the substrate misorientation is constructed. The inclusion of the ES barrier expands the region of island growth and shrinks the region of step-flow growth in the growth phase diagram. It is shown that the critical substrate temperature T, predicted by the model for the transition of layer-by-layer<---->step-flow growth can be fitted to the experimentally measured T-c approximate to 900 K at reasonable values of the parameters for elementary atomic events, the surface diffusion barrier and prefactor. The magnitudes of the surface diffusion barrier evaluated in the presence of the ES barrier are always less than that estimated in the absence of the ES barrier.