The basic version of the semimicroscopic particle-hole dispersive optical model is adopted and implemented to describe main properties of the Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei. Calculation results obtained for $^{48}\mathrm{Ca}, ^{90}\mathrm{Zr}, ^{132}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ are compared with available experimental data.