Critical behavior of the contact process in a multiscale network

TL;DR

This study explores the critical behavior of the contact process on a multiscale network combining chains and scale-free connections, revealing a new universality class with unique epidemic thresholds and lifetime divergences.

Contribution

It introduces a hybrid multiscale network model for the contact process, demonstrating a new universality class with distinct critical exponents and scaling behavior.

Findings

Finite epidemic threshold observed.

Exponential divergence of epidemic lifetime in subcritical phase.

Power law divergence of outbreak duration.

Abstract

Inspired by dengue and yellow fever epidemics, we investigated the contact process (CP) in a multiscale network constituted by one-dimensional chains connected through a Barab\'asi-Albert scale-free network. In addition to the CP dynamics inside the chains, the exchange of individuals between connected chains (travels) occurs at a constant rate. A finite epidemic threshold and an epidemic mean lifetime diverging exponentially in the subcritical phase, concomitantly with a power law divergence of the outbreak's duration, were found. A generalized scaling function involving both regular and SF components was proposed for the quasistationary analysis and the associated critical exponents determined, demonstrating that the CP on this hybrid network and nonvanishing travel rates establishes a new universality class.