The structure of coevolving infection networks

TL;DR

This paper analyzes how adaptive contact networks evolve during disease spread, revealing a stable degree distribution independent of initial network structure, through an analytic method applicable to various systems.

Contribution

It introduces a new analytical approach to determine the steady-state topology of coevolving infection networks, advancing understanding of their structural properties.

Findings

Infection networks reach a stable degree distribution regardless of initial topology.

The developed method accurately predicts network structure at equilibrium.

The approach applies broadly to various adaptive network systems.

Abstract

Disease awareness in infection dynamics can be modeled with adaptive contact networks whose rewiring rules reflect the attempt by susceptibles to avoid infectious contacts. Simulations of this type of models show an active phase with constant infected node density in which the interplay of disease dynamics and link rewiring prompts the convergence towards a well defined degree distribution, irrespective of the initial network topology. We develop a method to study this dynamic equilibrium and give an analytic description of the structure of the characteristic degree distributions and other network measures. The method applies to a broad class of systems and can be used to determine the steady-state topology of many other adaptive networks.