Chaotic and Stochastic Components in an Influenza Surveillance Series: Nonlinear Dynamics and Predictive Modeling...

Area of Science:

• Epidemiology
• Complex Systems
• Time Series Analysis

Background:

• Chaotic dynamics is increasingly studied in epidemiology, particularly for SARS-CoV-2, but less so for influenza.
• Existing research often filters noise from time series, potentially overlooking crucial epidemiological features within the noise.
• Dynamical noise in chaotic systems can offer insights for surveillance and risk analysis by revealing underlying nonlinear processes.

Purpose of the Study:

• To enhance empirical research on chaotic dynamics in influenza surveillance.
• To investigate the dynamical noise affecting chaotic influenza dynamics.
• To assess the implications for epidemiological risk analysis and surveillance.

Main Methods:

• Utilized weekly positive influenza test data (Northern Hemisphere, 2009-2025) from Our World in Data (WHO FluNet).
• Applied topological data analysis to reconstruct attractors and decompose dynamics into noise.
• Adapted methods for predictive decomposition in epidemiological risk analysis.

Main Results:

• Identified a low-dimensional chaotic attractor (fractal dimension 1-2) with a significant positive largest Lyapunov exponent.
• Observed power law scaling linked to long-wave outbreaks and nonstationary stochastic noise causing turbulent bursts.
• Achieved high prediction accuracy using machine learning: 92.11% (1 week), 85.95% (2 weeks), 81.75% (3 weeks), 77.59% (4 weeks), 73.35% (5 weeks).

Conclusions:

• Confirmed a 2-dimensional chaotic attractor in influenza surveillance data.
• Demonstrated the potential for up to 1-month predictions with high accuracy.
• Showcased a modeling approach for the attractor and noise, supporting uncertainty quantification and risk analysis.