Lyapunov Exponents, Nonlinear Dynamics, and the Analysis of Spatiotemporal Health Data for Policy and Interventions

Background: Epidemiological approaches to health and behavioral data having multiple follow-up assessments have relied upon time series analysis and repeated measures multivariate statistics, often with the assumption of linearity. Nonlinear dynamical analysis has been used extensively in the physical sciences and engineering but only with health-related continuous data such as cardiac rhythms and neuroendocrine cycles.

Purpose: We evaluated the utility of nonlinear analysis to periodic, discontinuous health data across five years of the National County Health Rankings in relationship to geospatial regression analyses with the goal of identifying parameters to model time-dependent layers of raster data.

Significance:  For health behaviors, the identification of convergence or divergence over time is valuable to evaluate Healthy People 2020 objectives and to identify facilitators and barriers for effective health interventions.

Methodology: We used R, Python, and GeoDa to perform temporal nonlinear return maps and geospatial regressions on 2010-2014 County Health Rankings data prepared by the University of Wisconsin Population Health Institute. Nonlinear analyses regarded the n = 3,221 county units as individual data points/cases within the phase space manifold of the nation’s health. Study variables included percentage obesity, smoking, child poverty rates, violent crime rates, infant mortality rates, and Ambulatory Care Sensitive Conditions (ACSC).

Conclusions: Temporally, most variables demonstrated stable steady state cycles, with obesity converging (Lyapunov exponent = -0.034) and ACSC diverging/repelling (Lyapunov exponent = 0.098). Spatial regression showed geographic patterns for these variables. Lyapunov exponents map the time trajectories of each variable, thus providing a tool for health policies and applied interventions.