Discovering Dynamic Patterns from Infectious Disease Data Using Dynamic Mode Decomposition

March 1, 2015

Abstract: 

Methods: Dynamic mode decomposition (DMD) is a recently developed method focused on discovering coherent spatial-temporal modes in high-dimensional data collected from complex systems with time dynamics. The algorithm has a number of advantages including a rigorous connection to the analysis of nonlinear systems, an equation-free architecture, and the ability to efficiently handle high-dimensional data.

Results: We demonstrate the method on three different infectious disease sets including Google Flu Trends data, pre-vaccination measles in the UK, and paralytic poliomyelitis wild type-1 cases in Nigeria. For each case, we describe the utility of the method for surveillance and resource allocation.

An illustration of the data collection and the dynamic mode decomposition (DMD) method. In the top panel, an illustration of how to construct the data matrices from numerical, laboratory, or historical data sources. The historical data illustration is of flu data for the US according to the Google Flu Trends tool. A longer description of the data is described in the Results section. The bottom panel illustrates the key components of solving for A: the singular value decomposition (SVD), the eigenvalue spectrum, and the dynamic modes. For infectious disease data, each of the elements of a dynamic mode will typically represent a specific geo-spatial location. The magnitude and phase of the element describes how the geo-spatial locations are related to each within that mode. If the mode has an associated eigenvalue with a nonzero imaginary component, indicating oscillatory behavior, then the angle of each element represents the relative phase of the location's oscillation relative to the other locations for that dynamic mode. This representation allows for a direct interpretation of the DMD output for disease spread: each dynamic mode identifies the locations involved in that dynamic pattern of disease spread as well as the relative phase of that location's peak infection time.

Conclusions: We demonstrate how DMD can aid in the analysis of spatial-temporal disease data. DMD is poised to be an effective and efficient computational analysis tool for the study of infectious disease.