title: Host-parasite models on graphs.
abstract: The behavior of two interacting populations "hosts" and "parasites" is investigated on Cayley trees and scale-free networks. In the former case analytical and numerical arguments elucidate a phase diagram for the susceptible-infected-susceptible model, whose most interesting feature is the absence of a tricritical point as a function of the two independent spreading parameters. For scale-free graphs, the parasite population can be described effectively by its dynamics in a host background. This is shown both by considering the appropriate dynamical equations and by numerical simulations on Barabási-Albert networks with the major implication that in the thermodynamic limit the critical parasite spreading parameter vanishes. Some implications and generalizations are discussed.
authors.affiliation: Laboratory of Physics, Helsinki University of Technology, P. O. Box 1100, 02015 HUT, Finland.
authors.forename: Matti
authors.initials: M
authors.lastname: Peltomäki
authors.forename: Ville
authors.initials: V
authors.lastname: Vuorinen
authors.forename: Mikko
authors.initials: M
authors.lastname: Alava
authors.forename: Martin
authors.initials: M
authors.lastname: Rost
mesh_terms: D000818:Animals; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D017753:Ecosystem; D006790:Host-Parasite Interactions; D006801:Humans; D008954:Models, Biological; D010272:Parasitic Diseases / Q000503:physiopathology*; D011157:Population Dynamics