To analyze recent experiments with a neodymium-doped fiber amplifier operating in the E-band of wavelengths (1350-1450 nm) and embedded in fused silica, we develop a time-dependent model consisting of rate equations for the aggregate ion populations and the radiation intensities along the amplifier axis. Both copropagating and counterpropagating intensities, including amplified spontaneous emission, are incorporated. The wavelength-dependent cross section for excited state absorption is inferred from auxiliary measurements. Steady-state solutions are obtained over a range of seed wavelengths and powers. The resulting gain curves agree with experiment at low to intermediate powers (less than ∼1 mW). With a proposed addition to the system loss, the agreement extends to saturation (∼100 mW).