Parameter Tuning for SIR-Related Models With Variational and Bayesian Methods Open Access

Abstract

The event of COVID-19 has put many mathematical models in competition to capture the disease's dynamic. The effectiveness of such a model is only possible with a process to tune its parameters for the available dataset. This thesis presents two methodologies --- Trust Region, a variational approach, and Ensemble Kalman Filter (EnKF), a Bayesian approach --- to solve the above issue. This project deals with the classical Susceptible, Infectious, and Recovered (SIR) epidemiology model and its variants. We compare the efficiency of our approaches through three SIR-related models: Epidemic SIR, Endemic SIR, and SIRW. Firstly, employing the variational method, especially the trust region method, and the PyBOBYQA algorithm, we fine-tune our models' parameters under noise-free and noise-inclusive conditions. Similarly, we utilize the Ensemble Kalman Filter method to explore the optimal sets for our models when white noise is presented and not presented. The results show that the Trust Region method performs well with the two basic SIR models under every condition, but this approach is not capable of handling more sophisticated models like SIRW. EnKF shows potential findings across the three models when the dataset is absent of noise. However, when a mild amount of noise is introduced, our optimization only shows success for the epidemic SIR and SIRW cases. With highly random datasets, we can only tune the correct parameters for the epidemic SIR model. This project serves as a first step in finding efficient optimization methodologies for nonlinear models under different conditions.

Table of Contents

Introduction Introduction to SIR-Related Models Epidemic SIR Model Endemic SIR Model SIRW Model Deterministic Approach Variational Method Trust Region (Derivative-Free) Variational Procedure With PyBOBYQA Epidemic SIR Model Endemic SIR Model SIRW Model Mixed Models Bayesian Approach Kalman Filter Method Ensemble Kalman Filter Results Endemic SIR Model Epidemic SIR Model SIRW Model Conclusion Discussion Trust Region Method Ensemble Kalman Filter Future Perspective Bibliography

About this Honors Thesis

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School	Emory College
Department	Mathematics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Applied Mathematics Mathematics
Keyword	SIRW Model SIR Models Trust Region PyBOBYQA Epidemic SIR Model Ensemble Kalman Filter Optimization Parameter Tuning Variational Method Endemic SIR Model
Committee Chair / Thesis Advisor	Alessandro Veneziani, Emory University
Committee Members	Elizabeth Newman, Emory University Talea L. Mayo, Emory University

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