Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19

Area of Science:

• Epidemiology
• Applied Mathematics
• Computational Biology

Background:

• Classical SIR models are foundational for epidemic dynamics but can be limited in capturing complex temporal patterns.
• Accurate modeling and forecasting of infectious diseases are crucial for public health interventions.
• The COVID-19 pandemic highlighted the need for advanced modeling techniques.

Purpose of the Study:

• To introduce epidemic-fitted wavelets as a novel tool for modeling epidemic dynamics.
• To develop a universal modeling framework based on wavelet theory and machine learning.
• To apply the developed method for modeling and forecasting the spread of COVID-19.

Main Methods:

• Development of epidemic-fitted wavelets, including infectious individuals (I(t)) and their derivatives.
• Application of a model selection method utilizing wavelet theory.
• Integration of machine learning-based curve fitting techniques for practical application.
• Utilizing the Johns Hopkins University dataset for empirical validation.

Main Results:

• Demonstrated the efficacy of epidemic-fitted wavelets in modeling epidemic dynamics.
• Successfully applied the method to forecast COVID-19 spread in various countries (France, Germany, Italy, Czech Republic) and US states (New York, Florida).
• Established universal models as finite linear combinations of epidemic-fitted wavelets.

Conclusions:

• Epidemic-fitted wavelets offer a powerful and flexible framework for epidemic modeling and forecasting.
• The combination of wavelet theory and machine learning provides a robust approach for analyzing real-world epidemic data.
• This method has significant potential for understanding and predicting the trajectory of infectious diseases.