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People change their physical contacts as a preventive response to infectiousdisease propagations. Yet, only a few mathematical models consider the coupleddynamics of the disease propagation and the contact adaptation process. Thispaper presents a model where each agent has a default contact neighborhood set,and switches to a different contact set once she becomes alert about infectionamong her default contacts. Since each agent can adopt either of two possibleneighborhood sets, the overall contact network switches among 2^N possibleconfigurations. Notably, a two-layer network representation can fully model theunderlying adaptive, state-dependent contact network. Contact adaptationinfluences the size of the disease prevalence and the epidemic threshold---acharacteristic measure of a contact network robustness against epidemics---in anonlinear fashion. Particularly, the epidemic threshold for the presentedadaptive contact network belongs to the solution of a nonlinearPerron-Frobenius (NPF) problem, which does not depend on the contact adaptationrate monotonically. Furthermore, the network adaptation model predicts acounter-intuitive scenario where adaptively changing contacts may adverselylead to lower network robustness against epidemic spreading if the contactadaptation is not fast enough. An original result for a class of NPF problemsfacilitate the analytical developments in this paper.

Contact Adaption during Epidemics: A Multilayer Network Formulation Approach