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Starting with stochastic rate equations for the fundamental interactionsbetween microbes and their viruses, we derive a mean field theory for thepopulation dynamics of microbe-virus systems, including the effects oflysogeny. In the absence of lysogeny, our model is a generalization of thatproposed 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 fieldcalculations to demographic fluctuations, we have compared our results withstochastic simulations using the Gillespie algorithm. Finally, we estimate therange of parameters that delineate the various steady states of our model.

Fixed points and limit cycles in the population dynamics of lysogenic viruses and their hosts