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Numerical modeling of heavily-erbium-doped fluoride fiber lasers is presented. Calculations from the model were compared with all previously reported experimental demonstrations of heavily-erbium-doped fluoride fiber lasers. Commensurate with recent modeling studies, good agreement with the measurements was achieved with the use of scaled-down rate parameters for energy transfer that corresponds to weaker interactions between Er3+ ions. For wavelength-fixed (grating) systems, we show that the measured saturation of the output power results from a combination of changes to the Boltzmann distribution arising from core temperature excursions and pump excited state absorption (ESA). In free-running systems, we show that inter-Stark level transitions that terminate on progressively higher Stark levels within the 4I13/2 manifold in part describe the non-saturating behavior of the output power at moderate pump levels. The model was used to investigate the influence of dopant concentration, pump wavelength, pump configuration, output coupling and background loss of the fiber on laser performance. In contrast to a number of previous modeling investigations, our results show that the slope efficiency steadily increases with increasing erbium concentration as a result of the reduced rates of energy recycling caused by the weakly interacting Er3+ ions. The highest slope efficiency was obtained for a pump wavelength of 983 nm due to reduced levels of ESA, however, for both free-running and wavelength-fixed arrangements of the laser, pump ESA may ultimately preclude significant power scaling.