Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed...

Area of Science:

• Epidemiology
• Computational Mathematics
• Machine Learning

Background:

• Epidemiological models are crucial for understanding disease spread.
• Traditional models often struggle with time-varying parameters and complex dynamics.
• Physics-informed neural networks (PINNs) offer a novel approach to address these limitations.

Purpose of the Study:

• To apply PINNs for identifying time-dependent parameters and fractional differential operators in epidemiological models.
• To analyze variations of the susceptible-infectious-removed (SIR) model, including fractional-order and time-delay models.
• To investigate the identifiability and uncertainty quantification for these models in real-world pandemic forecasting.

Main Methods:

• Utilized PINNs to analyze epidemiological models, including SIR variations.
• Incorporated fractional-order and time-delay dynamics into the models.
• Represented time-dependent parameters and fractional orders using neural networks.
• Applied the methodology to COVID-19 data from New York City, Rhode Island, Michigan, and Italy.

Main Results:

• Successfully inferred time-dependent parameters for integer-order and time-delay models.
• Determined time-dependent fractional derivative orders for fractional differential models.
• Demonstrated the capability of PINNs to simultaneously infer unknown parameters and unobserved dynamics.
• Quantified uncertainties associated with neural network predictions and control measures.

Conclusions:

• PINNs provide a powerful framework for enhancing epidemiological modeling.
• The method allows for the identification of complex, time-varying dynamics and parameters.
• Accurate forecasting of pandemic spread, like COVID-19, is achievable with improved model identifiability and uncertainty quantification.