Invasion of cooperative parasites in moderately structured host populations

Certain defence mechanisms of phages against the immune system their bacterial host rely on cooperation phages. Motivated by this example we analyse invasion probabilities cooperative parasites in moderately structured populations. We assume that hosts occupy vertices a configuration model and offspring move to neighbouring sites infect new hosts. Parasites (usually) reproduce only when infecting simultaneously then generate many offspring. In regime identify spatial scale population structure at which turns from being an unlikely highly probable event.