In this work, we consider a delay differential equations model for bacteriophage infection and discuss the robustness of the positive equilibrium with respect to stochastic perturbations of the environment using two different approaches. First, we provide analytical estimates of the population intensities of fluctuations by Fourier transform methods. Next, we simulate the strong solutions of the arising stochastic delay differential equations by numerical methods of order 1. Extensive numerical experiments suggest that a noisy environment for the bacteria population is much more destabilizing on the concentrations at the equilibrium point than a noisy environment for the phage.