Bacteria growing on surfaces appear to be profoundly more resistant to control by lytic bacteriophages than do the same cells grown in liquid. Here, we use simulation models to investigate whether spatial structure per se can account for this increased cell density in the presence of phages. A measure is derived for comparing cell densities between growth in spatially structured environments versus well mixed environments (known as mass action). Maintenance of sensitive cells requires some form of phage death; we invoke death mechanisms that are spatially fixed, as if produced by cells. Spatially structured phage death provides cells with a means of protection that can boost cell densities an order of magnitude above that attained under mass action, although the effect is sometimes in the opposite direction. Phage and bacteria self organize into separate refuges, and spatial structure operates so that the phage progeny from a single burst do not have independent fates (as they do with mass action). Phage incur a high loss when invading protected areas that have high cell densities, resulting in greater protection for the cells. By the same metric, mass action dynamics either show no sustained bacterial elevation or oscillate between states of low and high cell densities and an elevated average. The elevated cell densities observed in models with spatial structure do not approach the empirically observed increased density of cells in structured environments with phages (which can be many orders of magnitude), so the empirical phenomenon likely requires additional mechanisms than those analyzed here.