A size structured model for bacteria–phages interaction

We introduce a size structured pde model for susceptible and resistant bacteria populations that grow as they feed from a resource that is added at a constant rate. Bacteria populations evolve in the presence of a phages population that is adsorbed by the susceptible bacteria but also by a bulk population of phage free receptors on cell debris and on infected cells. Assuming that the individual cell growth is non negative, we compute an age function that allows us to change variables and to obtain an equivalent system with structure by the cell age and where the cell volume becomes a state variable. We characterize the steady states of these models.