Population decay (real transition) and pure dephasing (virtual transition) determine the dephasing rates of excitons in quantum-dot (QD) semiconductor optical amplifiers. In previous theoretical studies, population-decay and pure dephasing are usually handled separately. In this paper, the theory of exciton dephasing in an InAs/GaAs QD semiconductor optical amplifier is presented to elucidate the combination of population decay and pure dephasing and determine the total dephasing rate. The proposed model extends the classical independent boson model to include the effects of real transition. Results show that population decay decreases the pure dephasing rate and imply that the former is directly coupled to pure dephasing despite their differences. Our theoretical results are consistent with the reported experimental phenomena.