title: Modeling epidemics on adaptively evolving networks: A data-mining perspective.
abstract: The exploration of epidemic dynamics on dynamically evolving ("adaptive") networks poses nontrivial challenges to the modeler, such as the determination of a small number of informative statistics of the detailed network state (that is, a few "good observables") that usefully summarize the overall (macroscopic, systems-level) behavior. Obtaining reduced, small size accurate models in terms of these few statistical observables--that is, trying to coarse-grain the full network epidemic model to a small but useful macroscopic one--is even more daunting. Here we describe a data-based approach to solving the first challenge: the detection of a few informative collective observables of the detailed epidemic dynamics. This is accomplished through Diffusion Maps (DMAPS), a recently developed data-mining technique. We illustrate the approach through simulations of a simple mathematical model of epidemics on a network: a model known to exhibit complex temporal dynamics. We discuss potential extensions of the approach, as well as possible shortcomings.
authors.affiliation: a Department of Chemical and Biological Engineering ; Princeton University ; Princeton , NJ USA.
authors.forename: Assimakis A
authors.initials: AA
authors.lastname: Kattis
authors.affiliation: a Department of Chemical and Biological Engineering ; Princeton University ; Princeton , NJ USA.
authors.forename: Alexander
authors.initials: A
authors.lastname: Holiday
authors.affiliation: b Department of Mathematics ; Princeton University ; Princeton , NJ USA.
authors.forename: Ana-Andreea
authors.initials: AA
authors.lastname: Stoica
authors.affiliation: a Department of Chemical and Biological Engineering ; Princeton University ; Princeton , NJ USA.|c Program in Applied & Computational Mathematics; Princeton University ; Princeton , NJ USA.|d Institute for Advanced Study; Technische Universität München ; Garching , Germany.
authors.forename: Ioannis G
authors.initials: IG
authors.lastname: Kevrekidis
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D057225:Data Mining; D058872:Epidemics; D048088:Informatics / Q000379:methods; D008962:Models, Theoretical; D013597:Systems Analysis
keywords: SIS; adaptive networks; data mining; diffusion maps; epidemics; equation-free