Calibration and prediction for the inexact SIR model

Yan Wang; Guichen Lu; Jiang Du; Yan Wang; Guichen Lu; Jiang Du

doi:10.3934/mbe.2022128

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 3: 2800-2818. doi: 10.3934/mbe.2022128

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Calibration and prediction for the inexact SIR model

1.
School of Statistics and Data Science, Beijing University of Technology, Beijing 100124, China
2.
School of Science, Chongqing University of Technology, Chongqing 400054, China

Received: 29 October 2021 Revised: 20 December 2021 Accepted: 22 December 2021 Published: 13 January 2022

A Susceptible Infective Recovered (SIR) model is usually unable to mimic the actual epidemiological system exactly. The reasons for this inaccuracy include observation errors and model discrepancies due to assumptions and simplifications made by the SIR model. Hence, this work proposes calibration and prediction methods for the SIR model with a one-time reported number of infected cases. Given that the observation errors of the reported data are assumed to be heteroscedastic, we propose two predictors to predict the actual epidemiological system by modeling the model discrepancy through a Gaussian Process model. One is the calibrated SIR model, and the other one is the discrepancy-corrected predictor, which integrates the calibrated SIR model with the Gaussian Process predictor to solve the model discrepancy. A wild bootstrap method quantifies the two predictors' uncertainty, while two numerical studies assess the performance of the proposed method. The numerical results show that, the proposed predictors outperform the existing ones and the prediction accuracy of the discrepancy-corrected predictor is improved by at least $ 49.95\% $.
- Inexact SIR model,
- Gaussian Process model,
- Wild bootstrap,
- uncertainty quantification,
- Heteroscedastic noise,
- calibration
Citation: Yan Wang, Guichen Lu, Jiang Du. Calibration and prediction for the inexact SIR model[J]. Mathematical Biosciences and Engineering, 2022, 19(3): 2800-2818. doi: 10.3934/mbe.2022128

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Abstract

A Susceptible Infective Recovered (SIR) model is usually unable to mimic the actual epidemiological system exactly. The reasons for this inaccuracy include observation errors and model discrepancies due to assumptions and simplifications made by the SIR model. Hence, this work proposes calibration and prediction methods for the SIR model with a one-time reported number of infected cases. Given that the observation errors of the reported data are assumed to be heteroscedastic, we propose two predictors to predict the actual epidemiological system by modeling the model discrepancy through a Gaussian Process model. One is the calibrated SIR model, and the other one is the discrepancy-corrected predictor, which integrates the calibrated SIR model with the Gaussian Process predictor to solve the model discrepancy. A wild bootstrap method quantifies the two predictors' uncertainty, while two numerical studies assess the performance of the proposed method. The numerical results show that, the proposed predictors outperform the existing ones and the prediction accuracy of the discrepancy-corrected predictor is improved by at least $ 49.95\% $.

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