Stochastic Emergence of Irregular Infection Fronts in Motile Bacteria-Phage Populations

Interactions between bacteriophages and motile bacteria can produce irregular spatial patterns that deterministic models fail to capture. Here we show that these irregularities arise from stochastic infection dynamics at the single-cell level. We develop a discrete, stochastic model of phage–bacteria co-propagation, which represents bacteria and phages as non-negative integers on a two-dimensional lattice, while nutrients and attractants remain continuous fields. Stochastic rules govern bacterial growth, chemotactic movement, infection, and lysis, allowing spatial heterogeneity to emerge in agreement with experimentally observed asymmetric patterns. Simulations reveal that rare events, in which an infected bacterium migrates ahead of the front before lysis, locally seed new infection centers. The resulting front roughness is controlled by the product of burst size and adsorption rate, and is suppressed when the effective population size increases or the variability of latent period decreases. These results link microscopic stochasticity to emergent spatial structure in phage–bacteria populations.