Dimensionality reduction in epidemic spreading models

¹ Dipartimento di Ingegneria Elettrica, Elettronica e Informatica, University of Catania - Viale A. Doria 6, 95125 Catania, Italy
² Department of Mechanical and Aerospace Engineering, New York University Polytechnic School of Engineering, Six MetroTech Center - Brooklyn, NY 11201, USA
³ Dipartimento di Ingegneria Elettrica e dell'Informazione, Politecnico di Bari - Via E. Orabona 4, 70125 Bari, Italy

^(a) mfrasca@diees.unict.it
^(b) alessandro.rizzo@nyu.edu
^(c) lgallo@diees.unict.it
^(d) lfortuna@diees.unict.it
^(e) mporfiri@nyu.edu

Received: 3 August 2015
Accepted: 15 September 2015

Abstract

Complex dynamical systems often exhibit collective dynamics that are well described by a reduced set of key variables in a low-dimensional space. Such a low-dimensional description offers a privileged perspective to understand the system behavior across temporal and spatial scales. In this work, we propose a data-driven approach to establish low-dimensional representations of large epidemic datasets by using a dimensionality reduction algorithm based on isometric features mapping (ISOMAP). We demonstrate our approach on synthetic data for epidemic spreading in a population of mobile individuals. We find that ISOMAP is successful in embedding high-dimensional data into a low-dimensional manifold, whose topological features are associated with the epidemic outbreak. Across a range of simulation parameters and model instances, we observe that epidemic outbreaks are embedded into a family of closed curves in a three-dimensional space, in which neighboring points pertain to instants that are close in time. The orientation of each curve is unique to a specific outbreak, and the coordinates correlate with the number of infected individuals. A low-dimensional description of epidemic spreading is expected to improve our understanding of the role of individual response on the outbreak dynamics, inform the selection of meaningful global observables, and, possibly, aid in the design of control and quarantine procedures.