Calibration and prediction for the inexact SIR model

Area of Science:

• Epidemiology
• Statistical modeling
• Computational science

Background:

• Standard Susceptible Infective Recovered (SIR) models often fail to accurately represent real-world epidemiological systems due to inherent assumptions and data observation errors.
• Model discrepancies and heteroscedastic observation errors in reported case data limit the precision of traditional SIR models.

Purpose of the Study:

• To develop and evaluate novel calibration and prediction methods for the SIR model that account for model discrepancies and heteroscedastic errors.
• To propose two new predictors: a calibrated SIR model and a discrepancy-corrected predictor integrating Gaussian Process modeling.

Main Methods:

• Utilized Gaussian Process modeling to address model discrepancies in the SIR model.
• Developed a discrepancy-corrected predictor by combining a calibrated SIR model with Gaussian Process predictions.
• Employed a wild bootstrap method for quantifying prediction uncertainty.
• Conducted two numerical studies to assess the performance of the proposed methods.

Main Results:

• The proposed predictors demonstrated superior performance compared to existing methods.
• The discrepancy-corrected predictor achieved a significant improvement in prediction accuracy, exceeding 49.95%.
• Gaussian Process modeling effectively mitigated model discrepancies, enhancing predictive power.

Conclusions:

• The proposed calibration and prediction methods offer a substantial improvement for SIR epidemiological modeling.
• The discrepancy-corrected predictor provides more accurate and reliable forecasts for infectious disease dynamics.
• This approach enhances the utility of SIR models in real-world public health applications.