Characterising Steady-State Topologies of SIS Dynamics on Adaptive Networks

TL;DR

This paper analyzes the steady-state topologies of SIS epidemic models on adaptive networks, showing that in the endemic phase, the network's structure depends only on disease and rewiring parameters, not initial topology.

Contribution

It provides an analytical description of the steady-state network structure in SIS models on adaptive networks, highlighting independence from initial conditions.

Findings

Steady state depends only on disease and rewiring parameters

Network topology converges to a degree distribution determined by model parameters

Steady state is independent of initial network topology

Abstract

Disease awareness in epidemiology can be modelled with adaptive contact networks, where the interplay of disease dynamics and network alteration often adds new phases to the standard models (Gross et al. 2006, Shaw et al. 2008) and, in stochastic simulations, lets network topology settle down to a steady state that can be static (in the frozen phase) or dynamic (in the endemic phase). We show for the SIS model that, in the endemic phase, this steady state does not depend on the initial network topology, only on the disease and rewiring parameters and on the link density of the network, which is conserved. We give an analytic description of the structure of this co-evolving network of infection through its steady-state degree distribution.