MultiCoPat

Time-Frequency Dynamics of Influenza Co-circulation based on STL-AFD-CWT-WTC

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This repository contains the code and analysis pipeline for the study "Time-Frequency Dynamics of Influenza Co-circulation based on STL-AFD-CWT-WTC".

Abstract

Objective: Co-circulation of multiple influenza virus subtypes poses a major challenge to global public health surveillance and prediction. Although spatiotemporal heterogeneity in influenza transmission has been documented, the specific impact of viral co-circulation on non-stationary epidemic sequences remains poorly understood. This study aims to reveal the impact of co-circulation on influenza transmission systems and their coupling relationships with environmental driving factors through time-frequency analysis.

Methods: We integrated an analytical framework combining Seasonal-Trend decomposition using Loess (STL), Adaptive Fourier Decomposition (AFD), Continuous Wavelet Transform (CWT), and Wavelet Coherence (WTC). We analyzed 323 weekly influenza surveillance time series from China spanning 2011 to 2025, and quantitatively assessed the time-frequency coupling strength of 63,308 influenza-environment variable pairs.

Results: The study found that co-circulation periods and single-dominant periods have fundamentally different dynamic mechanisms, with co-circulation periods exhibiting a regime shift of the influenza system from order to chaos. During co-circulation periods, seasonality shift significantly increased, and high-intensity anomalous fluctuations emerged in the residual component. Furthermore, this study revealed significant north-south mechanism differences from a data perspective: northern regions exhibited "Environmental Locking", where even during co-circulation periods, epidemics remain strongly constrained by harsh climate; while southern regions showed "Environmental Decoupling", particularly during H3N2 co-circulation periods, where ecological competition between viruses surpassed environmental driving forces (such as humidity and temperature), leading to the failure of traditional environmental predictive factors.

Conclusions: The results of this study demonstrate the unique time-frequency state of influenza co-circulation periods. Influenza co-circulation is not simply a superposition of strains but triggers changes in the influenza transmission system. This indicates that public health strategies need to be context-adaptive: northern regions can continue to rely on meteorological warnings, while during co-circulation periods in southern regions, reliance on environmental indicators should be reduced, instead strengthening real-time etiological and serological surveillance.

Figure 1: The Four-Step Multi-Scale Analysis Framework (STL-AFD-CWT-WTC).

Key Findings

1. Regime Shift from Order to Chaos:

   • Co-circulation periods exhibit fundamentally different dynamic mechanisms compared to single-dominant periods.
   • During co-circulation, the influenza system undergoes a regime shift, characterized by significantly increased Seasonality Shift and the emergence of high-intensity anomalous fluctuations in the residual component.

   Figure 3: Comparison of STL dynamics between single-dominant and co-circulation periods. Note the increased residual volatility during co-circulation.

2. Spatiotemporal Heterogeneity:

   • Northern China ("Environmental Locking"): Epidemics remain strongly constrained by harsh climate conditions even during co-circulation periods.
   • Southern China ("Environmental Decoupling"): Ecological competition between viruses often surpasses environmental driving forces (such as humidity and temperature). This is particularly evident during H3N2 co-circulation periods, leading to the failure of traditional environmental predictive factors.

   Figure 6: Integrated statistical analysis showing distinct patterns between Northern and Southern China.

3. Implications for Public Health:

   • Strategies need to be context-adaptive.
   • North: Continue relying on meteorological warnings.
   • South: During co-circulation, reduce reliance on environmental indicators and strengthen real-time etiological and serological surveillance.

Methodology: The Four-Step Framework

The analysis pipeline follows a "divide-and-conquer" strategy:

1. STL Decomposition: Isolates macroscopic trends ($T_t$) and stable seasonality ($S_t$) from the original time series.
2. Adaptive Fourier Decomposition (AFD): Extracts physically meaningful transient components from high-frequency residuals ($R_t$) to capture nonlinear dynamics.
3. Continuous Wavelet Transform (CWT): Reveals time-frequency fingerprints of viral spread and transient features of subtype competition.
4. Wavelet Transform Coherence (WTC): Quantifies the dynamic coupling between influenza transmission and environmental drivers.

Repository Structure

• src/: Core analysis scripts implementing the methodology.

  • data_portal.py: Unified interface for loading and preprocessing data.
  • stl_decomposition.py: Step 1 - Seasonal-Trend decomposition.
  • AFD_analysis.py: Step 2 - Adaptive Fourier Decomposition.
  • cwt_analysis.py: Step 3 - Continuous Wavelet Transform.
  • wtc_analysis.py: Step 4 - Wavelet Coherence.
  • comprehensive_analysis.py: Integrated statistical analysis and pattern recognition.

• figures/: Scripts to reproduce the figures in the manuscript.

  • plot_figure*.py: Scripts for specific figures (e.g., Figure 3: STL Dynamics Comparison).
  • utils.py: Shared plotting utilities.

• robustness/: Scripts for sensitivity analysis.

  • robustness_runner.py: Driver for robustness experiments (Baseline, Conservative, Sensitive, Ablation scenarios).

• data/: Directory for input data and processed results.

Installation

1. Clone the repository:

   git clone https://github.com/Hylouis233/MultiCoPat.git
   cd MultiCoPat

2. Install dependencies:

   pip install -r requirements.txt

Usage

1. Data Preparation

Place your raw data in the data/ directory.

2. Run Analysis Pipeline

Execute the core analysis scripts in order:

python src/stl_decomposition.py
python src/AFD_analysis.py
# ... and so on

3. Reproduce Figures

To generate the figures (e.g., Figure 3):

python figures/plot_figure3_stl_comparison.py

The outputs will be saved in results/figures/.

4. Run Robustness Checks

python robustness/robustness_runner.py