A combined neural ODE-Bayesian optimization approach to resolve dynamics and estimate parameters for a modified SIR...

Area of Science:

• Epidemiology
• Computational Biology
• Mathematical Modeling

Background:

• Traditional epidemiological models often simplify disease dynamics.
• Incorporating factors like immune memory and time delays is crucial for accurate infectious disease modeling.
• Existing methods may struggle with complex integro-differential equations and parameter estimation.

Purpose of the Study:

• To develop a novel hybrid approach integrating Neural Ordinary Differential Equations (NODEs) with Bayesian optimization.
• To model and estimate parameters for a modified time-delay Susceptible-Infected-Removed (SIR) model that includes immune memory.
• To enhance prediction accuracy for both short-term and long-term infectious disease dynamics.

Main Methods:

• A hybrid approach combining NODEs with Bayesian optimization was proposed.
• A modified time-delay SIR model with immune memory was formulated as an integro-differential equation.
• The NODE framework was extended using a Runge-Kutta solver to handle convolution integrals for parameter and dynamics learning.
• Bayesian optimization was employed to improve prediction accuracy, particularly for long-term dynamics.

Main Results:

• The hybrid model successfully learned time-dependent parameters from COVID-19 data for Mexico, South Africa, and South Korea.
• Accurate short-term and long-term predictions of infection dynamics were achieved.
• The model demonstrated the capability to predict infection peaks with significant lead time.

Conclusions:

• The proposed hybrid NODEs and Bayesian optimization approach offers a powerful tool for analyzing and predicting infectious disease outbreaks.
• This methodology effectively captures complex dynamics, including time delays and immune memory, in epidemiological models.
• The findings provide valuable insights for public health responses through early and accurate prediction of infection peaks.