  Starting with stochastic rate equations for the fundamental interactions
between microbes and their viruses, we derive a mean field theory for the
population dynamics of microbe-virus systems, including the effects of
lysogeny. In the absence of lysogeny, our model is a generalization of that
proposed phenomenologically by Weitz and Dushoff. In the presence of lysogeny,
we analyze the possible states of the system, identifying a novel limit cycle,
which we interpret physically. To test the robustness of our mean field
calculations to demographic fluctuations, we have compared our results with
stochastic simulations using the Gillespie algorithm. Finally, we estimate the
range of parameters that delineate the various steady states of our model.
