Pathogen transmission at stage-structured infectious patches: Killers and vaccinators

Spatial localization of an obligate-killing, free-living pathogen generates a landscape of patches where new infections occur. As an infectious patch ages, both pathogen exposure at the patch and the probability of lethal infection following exposure can decline. We model stage-structured infectious patches, where non-lethal exposure can naturally "vaccinate" susceptible hosts. We let the between-stage difference in pathogen transmission, and then the between-stage difference in patch virulence, increase independently of other parameters. Effects of increasing either between-stage difference (about a fixed mean) depend on the probability a patch transitions from the first to second stage, i.e., the chance that a killer patch becomes a vaccinator. For slower stage transition, greater between-stage differences decreased susceptibles, and increased both resistant-host and killer patch numbers. But our examples reveal that each effect can be reversed when between-stage transition occurs more rapidly. For sufficiently rapid stage transition, increased between-stage virulence differences can lead to pathogen extinction, and leave the host at disease-free equilibrium. The model's general significance lies in demonstrating how epidemiological variation among sites of environmentally transmitted disease can strongly govern host-parasite dynamics.