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A numerical model that accounts for the effects of the amplified spontaneous emission (ASE) on the carrier dynamics in a travelling wave semiconductor optical amplifier is presented. The ASE is modeled using effective parameters that are derived starting from the spontaneous emission and gain models. The gain dynamics are then analyzed using the parameters extracted from measurements on a real device to explain the overshoot in the gain recovery. The model is also used to simulate the gain recovery in a three-wavelength device configuration for various injected powers and wavelengths. The recovery time when the injected beam is at the device transparency wavelength is also analyzed with particular attention to the differences between co- and counter-propagating configurations.