Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction

Ecological interactions between species that prefer different habitat types but come into contact in edge regions at the interfaces between habitat ty pes are modeled via reaction-diffusion systems. The primary sort of interac tion described by the models is competition mediated by pathogen transmissi on. The models are somewhat novel because the spatial domains for the varia bles describing the population densities of the interacting species overlap but do not coincide. Conditions implying coexistence of the two species or the extinction of one species are derived. The conditions involve the prin cipal eigenvalues of elliptic operators arising from linearizations of the model system around equilibria with only one species present. The condition s for persistence or extinction are made explicit in terms of the parameter s of the system and the geometry of the underlying spatial domains via esti mates of the principal eigenvalues. The implications of the models with res pect to conservation and refuge design are discussed.