A Modified PINN Approach for Identifiable Compartmental Models in Epidemiology with Application to COVID-19

Area of Science:

• Epidemiology and Public Health
• Computational Biology and Bioinformatics
• Machine Learning and Artificial Intelligence

Background:

• Compartmental models, including the Susceptible-Infected-Confirmed-Recovered-Deceased (SICRD) model, are crucial for understanding infectious disease dynamics like COVID-19.
• Machine learning (ML) applications to these epidemiological models have shown significant promise in improving predictive accuracy and parameter estimation.
• Accurate estimation of the infected population and model parameters is vital for effective pandemic response and policy-making.

Purpose of the Study:

• To estimate the unknown infected compartment (I) and several unknown parameters within the SICRD compartmental model for COVID-19.
• To develop and validate a novel modification of Physics-Informed Neural Networks (PINNs) for enhanced epidemiological modeling.
• To assess the performance of the modified PINN in handling complex scenarios with multiple unknown variables and time-varying parameters.

Main Methods:

• Utilized the Susceptible-Infected-Confirmed-Recovered-Deceased (SICRD) compartmental model as the foundational epidemiological framework.
• Applied a modified Physics-Informed Neural Network (PINN) approach, incorporating a wavelet transform for data preprocessing.
• Introduced a novel modification to the PINN's loss function to reduce the number of simultaneously estimated unknowns, improving identifiability and stability.

Main Results:

• The modified PINN demonstrated stable, efficient, and accurate estimation of infected individuals and model parameters, outperforming the unmodified network.
• The enhanced network successfully handled scenarios with multiple unknown variables, a common challenge in complex epidemiological models.
• The model's efficiency allowed for application to time-varying parameter estimation and was used to rank states by estimated relative testing efficiency.

Conclusions:

• The modified PINN approach offers a robust and effective solution for estimating key variables and parameters in compartmental epidemiological models.
• This novel loss function modification significantly enhances the stability and accuracy of ML-based epidemiological modeling, particularly with numerous unknowns.
• The method's efficiency and accuracy provide a valuable tool for real-time pandemic analysis, policy evaluation, and comparative state-level assessments.