Host-parasite models on graphs.


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.

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@article{Peltomki2005HostparasiteMO, title={Host-parasite models on graphs.}, author={Matti Peltom{\"a}ki and Ville Vuorinen and Mikko Alava and Martin Rost}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2005}, volume={72 4 Pt 2}, pages={046134} }