A new form of the transfer equations (TE) is proposed based on theoretical studies, strictly speaking, a system of TE describing the process of wide-band radiation transfer in disperse media. Within the limits of the Monte Carlo method, an algorithm has been developed for numerically solving the above-mentioned TE system, which allows one to calculate the spatiotemporal and spectral characteristics of laser-induced fluorescence (LIF) under boundary conditions corresponding to real experiments. Numerical estimates obtained demonstrate the efficiency of the proposed method and confirm the necessity of taking into account the background due to multiple scattering in systems with wide field-of-view receiving optics. Further studies will deal with the account of the phenomena of resonance energy transfer at spontaneous fluorescence in multicomponent systems.