<p>Bacteriophages strongly influence the spatial structure of microbial communities. Their interactions with motile bacteria can produce irregular patterns, but underlying mechanisms remain unclear. 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 on a two-dimensional lattice, in which bacteria and phages populations are represented as integers, while nutrients and attractants are treated as real-valued fields. Stochastic rules governing growth, chemotaxis, infection, and lysis allow spatial heterogeneity to emerge. Simulations reveal that rare events, in which an infected bacterium migrates ahead of the front before lysis, 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 per lattice site increases or variability of latent period decreases. These results link microscopic stochasticity to emergent spatial structure in phage-bacteria populations.</p>