Unlike semiconductor lasers that always operate within a narrow band in frequency domain, semiconductor optical amplifiers (SOAs) normally operate in a much broader area. The noise characteristic is also crucial for amplifier design. The study of the dynamic interaction among the signal channels and noise in SOAs is therefore highly demanded. In this work, a time-domain model is implemented based on the combination of the traveling wave equation, the effective Bloch equation and the modified carrier rate equation. The optical field propagation is described by the traveling wave equation. The interaction between the optical field and the polarization is treated by the effective Bloch equation hence both homogeneous and inhomogeneous gain broadenings over the entire operating frequency range is naturally considered. Finally, the carrier rate equation is modified to make the model self-sustaining. This model has the spontaneous emission noise incorporated hence effects such as noise introduced gain saturation, beatings among different signal channels and the noise are all captured. The key feature of this model is its capability of handling the signal-signal and the signal-noise indirect and direct interactions, generated by the mutual power saturation and the spectral hole burning (SHB), respectively. This model is implemented and validated through comparisons, and is also applied for the simulation of a typical SOA with an assumed operating condition that can hardly be treated accurately by other existing models.