Erbium-doped materials have played an important role in the fabrication of light sources used in silicon photonics. Recent studies demonstrated that erbium silicate nanowire had a high net gain attributable to its high erbium concentration and excellent material quality. We establish a more accurate and comprehensive theoretical model of erbium silicate nanowire, analyze the modeled nanowire's properties, and optimize a high-gain erbium silicate waveguide amplifier and low-threshold, high-efficiency laser by considering upconversion, energy transfer, and amplified spontaneous emission. The simulation results and previous experimental data reported in reference showed some agreement. A proposed waveguide amplifier, based on the optimized design, displayed a gain greater than 20 dB/mm. Then, a 3.3 mW low-threshold laser with a maximum power-conversion efficiency of 50% was modeled by choosing the optimized resonator cavity and reflector. The results indicate that erbium silicate compound materials with large optical gains can serve as potential candidates for inclusion in scale-integrated amplifiers and other applications requiring lasers.