M13 bacteriophage is a bacterial virus that improves the gut microbiome. As such, this type of bacteriophage is important to food and agricultural industries. To produce large batches of bacteriophage, E. coli must be infected with the bacteriophage and then placed in optimal living environments.

A lot of research has focused on finding the optimal environment for E. coli to produce bacteriophage in, but very little attention has been directed to the behavior of infected E. coli in sub-optimal environments. We use ordinary differential equations to model the population dynamics of E. coli  and bacteriophage in these new environments.