The distributed gain of single- and dual-wavelength-pumped thulium-doped fiber amplifiers is modeled. The excellent agreement between the model and coherent optical frequency domain reflectometry measurements enables us to estimate intrinsic loss, branching ratios of fluorescence originating from the 3H4 level, and cross sections of upconversion pumping at 1050 and 1410 nm for the Tm3+ ions in the fiber. With the branching ratios obtained it is possible to describe induced signal absorption when pumping at 800 nm.