We propose a model for phage-host interactions in which the environment is broken into two compartments. The first compartment consists of the particulate organic matter (POM), where bacteria grow to high densities. The second compartment is the aquatic phase, where the bacteria are not growing due to lack of nutrients. We will consider bacterial populations to be under the influence of two mechanisms of control; namely phage and eukaryotic grazers. The eukaryotic grazers will be modeled as exponential decay rates, with the important detail that they will be assumed to prey preferentially on the bacteria that are active or bigger. Phage infections will be modeled as mass-action processes, with bacteria undergoing lysis after a certain time and giving rise to new phage particles. It will be further assumed that bacteria can only be infected (or lysed) on the particle compartment. Using this heterogeneous landscape, we study two cases, a strictly lytic phage and a lysogenic one, to determine some of the conditions under which a ratio of 10 phage particles per bacterial host can be maintained in the aquatic environment. The equations can be written as:
Here P, I and S denote the populations of bacteriophage, infected and susceptible bacteria respectively. A subindex A denotes that the quantity is measured on the "particle" compartment, while a subindex B denotes that the quantity is measured on the "inter-particle" compartment. The meaning of the parameter are as follows: γ is the decay rate for phage, β is the burst size for infected bacteria undergoing lysis, κ is the contact rate in the "particle" compartment, r is the growth rate in the particle compartment, g is the grazing rate due to protests, λ is the decay rate due to lysis and mb denotes bacterial migration between compartments. For a strictly lytic phage equation (4) and the migration terms on equation (2) do not exist.
Forest Rohwer, San Diego State University