The propagation of events or influence in small-world networks is a very important issue. Based on previous researches, we study the case that the propagation is driven by noise. We establish a model which is a generalized Fokker-Planck equation(FPE) about the evolution probability of influence volume. In order to make it more practical, coefficients in the FPE are made time-dependent. We found the algebraic structure and dynamical symmetry of this FPE. By means of algebraic dynamics theory, the exact solutions of this FPE are presented. At last, the evolution of the probability of the influence volume is considered.