Well-posedness and dissipativity for a model of bacteriophage and bacteria in a flow reactor

The Levin-Stewart model of bacteriophage predation of bacteria in a chemostat is modified for a flow reactor in which bacteria are motile, phage diffuse, and advection brings fresh nutrient and removes medium, cells and phage. A fixed latent period for phage results in a system of delayed reaction-diffusion equations with non-local nonlinearities. We show that the model generates a well-posed dynamical system which has a compact global attractor.