This paper investigates the dynamics of a chemostat model incorporating two populations of one bacterial species: susceptible and virus-infected. Through the two operating parameters of the model, represented by the input concentration of the nutrient and the dilution rate of the chemostat, we analyze the existence and stability conditions of all possible equilibria, and then describe the operating diagram of the model, which is the bifurcation diagram giving its behavior with respect to those operating parameters, that visually depicts the various regions of stability of those equilibria. This diagram gives a better understanding of the complex interplay between bacterial populations growth, viral infection and environmental factors, in a controlled environment.