Self-organized coexistence of phage and a population of host colonies

Phages and bacteria coexist under widely different conditions, ranging from liquid cultures to oceans, soil, and the human gut. However, our models are typically limited to well-mixed liquid cultures governed by mass-action kinetics. Here, we suggest a modification to the Lotka-Volterra dynamics by including the formation of microcolonies. By analyzing the model in an open system with a steady influx of bacteria, we predict that the colony size distribution is power-low distributed with steeper exponents for the stronger external influx. In the realistic case where the phage attack rate to individual colonies is proportional to their radius, we obtain self-organization to a steady state where the maximal colony size is smaller for stronger external driving.