  People change their physical contacts as a preventive response to infectious
disease propagations. Yet, only a few mathematical models consider the coupled
dynamics of the disease propagation and the contact adaptation process. This
paper presents a model where each agent has a default contact neighborhood set,
and switches to a different contact set once she becomes alert about infection
among her default contacts. Since each agent can adopt either of two possible
neighborhood sets, the overall contact network switches among 2^N possible
configurations. Notably, a two-layer network representation can fully model the
underlying adaptive, state-dependent contact network. Contact adaptation
influences the size of the disease prevalence and the epidemic threshold---a
characteristic measure of a contact network robustness against epidemics---in a
nonlinear fashion. Particularly, the epidemic threshold for the presented
adaptive contact network belongs to the solution of a nonlinear
Perron-Frobenius (NPF) problem, which does not depend on the contact adaptation
rate monotonically. Furthermore, the network adaptation model predicts a
counter-intuitive scenario where adaptively changing contacts may adversely
lead to lower network robustness against epidemic spreading if the contact
adaptation is not fast enough. An original result for a class of NPF problems
facilitate the analytical developments in this paper.
