A dedicated 3D numerical model based on coupled mode theory and solving the rate equations has been developed to analyse, design and optimize an optical amplifier obtained by using a tapered fiber and a Er³⁺-doped chalcogenide microsphere. The simulation model takes into account the main transitions among the erbium energy levels, the amplified spontaneous emission and the most important secondary transitions pertaining to the ion-ion interactions. The taper angle of the optical fiber and the fiber-microsphere gap have been designed to efficiently inject into the microsphere both the pump and the signal beams and to improve their spatial overlapping with the rare earth doped region. In order to reduce the computational time, a detailed investigation of the amplifier performance has been carried out by changing the number of sectors in which the doped area is partitioned. The simulation results highlight that this scheme could be useful to develop high efficiency and compact mid-infrared amplifiers.