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Gene regulation is an intrinsically noisy process, which is subject to intracellular and extracellular noise perturbations and environment fluctuations. In this brief, we consider a stochastic nonlinear model for genetic regulatory networks with SUM regulatory functions. Based on the Lyapunov method and the Lur'e system approach, sufficient conditions for the stochastic stability of the genetic networks with disturbance attenuation are derived. The case with time delays owing to the slow processes of transcription, translation, and translocation is also studied. All the results are presented in terms of linear matrix inequalities (LMIs).