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

TL;DR

This paper develops a mean field theory for microbe-virus population dynamics including lysogeny, revealing a novel limit cycle and validating results with stochastic simulations.

Contribution

It introduces a new mean field model incorporating lysogeny effects and identifies a novel limit cycle in the system's dynamics.

Findings

Identification of a new limit cycle in lysogeny-including models

Validation of mean field results with Gillespie stochastic simulations

Estimation of parameter ranges for different steady states

Abstract

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.