Stochastic Chaos in Influenza Data – An Application of Topological Methods

Empirical methods of chaos theory have been applied to epidemiological data, uncovering evidence of chaos. In the current work, we apply, to the weekly share of positive tests for influenza in the Northern Hemisphere, an empirical methodology for studying stochastic chaos using topological data analysis methods combining chaos theory, topological machine learning, and nonlinear time series analysis for attractor reconstruction and decomposition to decompose a stochastic chaotic dynamics down to the independent and identically distributed (IID) noise. A stochastic chaotic attractor is found for the epidemiological series comprised of an interacting chaotic dynamics and a nonlinear stochastic component with nonstationary variance; the full dynamics is researched down to the IID noise, and the resulting estimated model is used to analyze major risk metrics, including probability dynamics and changing volatility. The implications for epidemiological empirical studies applying chaos theory to epidemiological data are discussed.