Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks

TL;DR

This study shows that the critical properties of a contact process on metapopulation networks are unaffected by local population structure, confirming the universality of reaction-diffusion models across different local configurations.

Contribution

It demonstrates through simulations and theory that local population structure does not influence the critical behavior of reaction-diffusion processes on complex networks.

Findings

Critical properties are independent of local population structure.

Numerical critical exponents match heterogeneous mean field theory.

Universality of reaction-diffusion models confirmed across structures.

Abstract

We investigate the effects of local population structure in reaction-diffusion processes representing a contact process (CP) on metapopulations represented as complex networks. Considering a model in which the nodes of a large scale network represent local populations defined in terms of a homogeneous graph, we show by means of extensive numerical simulations that the critical properties of the reaction-diffusion system are independent of the local population structure, even when this one is given by a ordered linear chain. This independence is confirmed by the perfect matching between numerical critical exponents and the results from a heterogeneous mean field theory suited, in principle, to describe situations of local homogeneous mixing. The analysis of several variations of the reaction-diffusion process allow to conclude the independence from population structure of the critical properties of CP-like models on metapopulations, and thus of the universality of the reaction-diffusion description of this kind of models.