Host--parasite models on graphs

TL;DR

This paper investigates host-parasite interactions on different network structures, revealing unique phase behaviors on Cayley trees and scale-free networks, with implications for understanding epidemic thresholds.

Contribution

It provides analytical and numerical analysis of host-parasite dynamics on Cayley trees and scale-free networks, highlighting the absence of a tri-critical point and the vanishing critical threshold.

Findings

No tri-critical point on Cayley trees.

Critical parasite spreading parameter vanishes on scale-free networks.

Parasite dynamics follow SIS model in a host background.

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, whose most interesting feature is the absence of a tri-critical point as a function of the two independent spreading parameters. For scale-free graphs, the parasite population can be described effectively by Susceptible-Infected-Susceptible-type dynamics in a host background. This is shown both by considering the appropriate dynamical equations and by numerical simulations on Barab\'asi-Albert networks with the major implication that in the termodynamic limit the critical parasite spreading parameter vanishes.