A mathematical model of marine bacteriophage evolution

To explore how particularities of a cell-virus system affects viral evolution, we formulate a mathematical model of marine bacteriophage evolution. The intrinsic simplicity of real-life phage-bacteria systems allows to have a reasonably simple model. The model constructed in this paper is based upon Beretta-Kuang model of bacteria-phage interaction. Compared to the Beretta-Kuang model, the model assumes the existence of a multitude of viral variants which correspond to continuously distributed phenotypes. It is noteworthy that this model does not include any explicit law or mechanism of evolution; instead it is assumed, in agreement to the principles of Darwinian evolution, that evolution in this system can occur as a result of random mutations and natural selection. Simulations with a leaner fitness landscape (which is chosen for the convenience of demonstration only) show that a pulse-type traveling wave moving towards increasing Darwinian fitness appears in the phenotype space. T...