Starting from the standard three-wave SBS coupled equations, we derive a novel expression describing Brillouin interaction between a pulsed pump wave with a finite cw component, and a Stokes continuous wave counter-propagating along a single-mode optical fiber. The derived integral equation relates the time-domain Stokes beam amplification to the Brillouin frequency distribution. The proposed model permits an accurate description of the Brillouin interaction even for arbitrarily-shaped pump pulses, and can be efficiently employed for improving the accuracy and the resolution of SBS-based distributed sensors. The validity and the limits of the proposed model are numerically analyzed and discussed.