The structure of coevolving infection networks

¹ Centro de Física da Matéria Condensada and Departamento de Física, Faculdade de Ciências da Universidade de Lisboa - P-1649-003 Lisboa, Portugal, EU
² Centro de Matemática e Aplicações Fundamentais, Faculdade de Ciências da Universidade de Lisboa P-1649-003 Lisboa, Portugal, EU

^a anunes@ptmat.fc.ul.pt

Received: 3 September 2011
Accepted: 21 November 2011

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 distribution 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.