Nonlinear frequency analysis of COVID-19 spread in Tokyo using empirical mode decomposition

📄 Paper Overview

This repository provides the reproduction code and examples for the research paper published in Scientific Reports (Nature Portfolio). The study applies Empirical Mode Decomposition (EMD) to analyze the nonlinear frequency characteristics of COVID-19 spread patterns in Tokyo.

For detailed research findings and scientific interpretations, please refer to the original paper: DOI: 10.1038/s41598-022-06071-8

🔬 Methodology

Empirical Mode Decomposition (EMD)

This study uses the PyEMD library (developed by Dawid Laszuk) for signal decomposition. EMD is a data-driven method that decomposes non-stationary signals into intrinsic mode functions without requiring predetermined basis functions.

Key EMD Properties:

• Adaptive and data-driven decomposition
• No assumptions about signal stationarity
• Preservation of temporal localization
• Complete signal reconstruction capability

Data Source

• Dataset: Tokyo COVID-19 daily confirmed cases
• Source: Japan Ministry of Health, Labour and Welfare
• Period: April 30, 2020 - October 6, 2021 (525 days)
• Coverage: Complete epidemic evolution including multiple waves

🚀 Reproduction Guide

Prerequisites

# Clone the repository
git clone https://github.com/yourusername/COVID19_EMD_Analysis.git
cd COVID19_EMD_Analysis

# Setup environment (recommended: conda)
conda env create -f environment.yml
conda activate covid19_emd_analysis

# Alternative: pip installation
pip install -r requirements.txt

Required Dependencies

numpy >= 1.19.0
scipy >= 1.5.0
matplotlib >= 3.3.0
pandas >= 1.1.0
EMD-signal >= 1.4.0  # PyEMD library for EMD implementation

Repository Structure

COVID19_EMD_Analysis/
├── data/20211006/             # Original COVID-19 dataset
├── src/                       # Analysis modules
│   ├── data_loader.py        # Data preprocessing
│   ├── emd_analyzer.py       # EMD analysis implementation  
│   ├── visualization.py     # Plotting and visualization
│   └── PyEMD/               # EMD library (external)
├── examples/                  # Reproduction examples
│   ├── covid19_emd_analysis_example.py  # Complete reproduction
│   └── simple_demo.py                   # Quick demonstration
└── results/                   # Generated outputs

📈 Step-by-Step Reproduction

Step 1: Data Loading and Preprocessing

The analysis begins with Tokyo's daily COVID-19 infection data. The raw data captures the complete pandemic evolution including multiple epidemic waves.

from src.data_loader import DataLoader

# Load the same dataset used in the paper
loader = DataLoader(data_path="data")
covid_data = loader.load_tokyo_covid_data("20211006", days=525)
daily_infections = covid_data['infections']

Original Signal Characteristics:

• First Wave (Apr-May 2020): Initial outbreak with peak ~400 cases/day
• Summer 2020 (Jul-Aug): Second wave reaching ~500 cases/day
• Winter Wave (Nov 2020 - Feb 2021): Major surge peaking at ~2,500 cases/day
• Spring 2021 (Apr-May): Moderate increase with ~1,000 cases/day
• Delta Wave (Jul-Sep 2021): Largest outbreak exceeding 5,700 cases/day
• Rapid Decline (Sep-Oct 2021): Sharp decrease to near-zero levels

Step 2: EMD Decomposition Analysis

The core analysis applies EMD to decompose the infection time series into intrinsic mode functions, exactly as described in the paper.

from src.emd_analyzer import EMDAnalyzer

# Perform EMD analysis with paper parameters
analyzer = EMDAnalyzer()
results = analyzer.analyze_signal(daily_infections, "tokyo_covid_infections")
imfs = results['imfs']
statistics = results['statistics']

The EMD decomposition yields 6 IMFs + residual. Each IMF captures different temporal scales in the epidemic dynamics, from daily fluctuations to long-term trends.

Step 3: Frequency Domain Analysis

The paper emphasizes the frequency characteristics revealed by EMD:

# Reproduce frequency analysis from paper
freq_analysis = results['statistics']
for i, (freq, period) in enumerate(zip(freq_analysis['mean_frequencies'], 
                                     freq_analysis['mean_periods'])):
    if freq > 0:
        print(f"IMF{i+1}: {freq:.4f} Hz (Period: {period:.1f} days)")

Step 4: Hilbert Spectrum Analysis

Advanced time-frequency analysis as presented in the paper:

# Generate Hilbert spectrum analysis
visualizer = EMDVisualizer()
hilbert_fig = visualizer.plot_hilbert_spectrum(
    results['frequencies'],
    results['amplitudes'], 
    dates=covid_data['formatted_dates'],
    title="COVID-19 Hilbert Spectrum - Paper Reproduction"
)

🚀 Quick Reproduction

For immediate reproduction of paper results:

# Run complete analysis reproducing all paper figures
python examples/covid19_emd_analysis_example.py

# Quick demonstration of key findings  
python examples/simple_demo.py

Both scripts will generate the exact visualizations and statistical results presented in the paper.

📄 License

This reproduction code is provided under MIT License for research and educational purposes.

📚 Citation

Primary Paper:

@article{dong2022nonlinear,
  title={Nonlinear frequency analysis of COVID-19 spread in Tokyo using empirical mode decomposition},
  author={Dong, Ran and Ni, Shaowen and Ikuno, Soichiro},
  journal={Scientific Reports},
  volume={12},
  number={1},
  pages={2175},
  year={2022},
  publisher={Nature Publishing Group UK London}
}

🔗 Related Resources

• Paper: Scientific Reports DOI: 10.1038/s41598-022-06071-8
• Original Dataset: Japan MHLW COVID-19 Data
• EMD Library: PyEMD Documentation

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For questions about reproduction: This code faithfully reproduces the methods and results described in the Scientific Reports paper. For methodological questions, please refer to the original publication.