Estimating and Predicting the Effect of Quarantine in the COVID-19 Pandemic: Using a Modified SEIR Model Open Access

Abstract

Governmental policies are one of the determining factors in slowing down the spread of the COVID-19 pandemic. It has been shown that effective government regulations, such as the mandate to wear masks, can control the development of the pandemic. This study aims to estimate the effectiveness of quarantine policies in the process of slowing down the pandemic.

For this study, we used the data from Wuhan, Italy, and South Korea after the cumulative confirmed cases in each region has exceeded 500 with a total period of 80 days. First, we replicated previous research on modeling the pandemic using a modified Susceptible-Infectious-Recovered-Quarantined epidemiological model. However, since this model does not consider the transformation from the “Quarantined” state to other states, we found the predicted quarantined population is too large to be realistic. Given this, we proposed a new model that estimates the quarantine strength directly from data and uses an LSTM network to make predictions for future periods. Several limitations with our model are its error sensitivity, model generalizability, and interpretability.

Through this study, we also realized that sometimes we might face the trade-off between the model interpretability and generalizability: a generic model like neural networks suffers from low interpretability, while a specific model may not apply to all situations. The best case is that we can recover the governing equations from the dataset directly. As an example to show this is possible, we used the Sparse Identification of Nonlinear Dynamics (SINDy) method to successfully recover the equations of the standard SIR model based on its trajectory.

Table of Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Contributions and Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 SIR-based Models under Consideration of Quarantine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Introduction to Susceptible-Infectious-Recovered Epidemiological Models . . . . . . . . . . 5

2.2 Modeling with the SIRQ Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 SEIR-based Models for Quarantine Strength Estimation and Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Model Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Training Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 Neural Network Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.5 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4 Recovering the Governing Equations Using Sparse Identification of Nonlinear Dynamics (SINDy) Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

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 Computer Science
Keyword	COVID-19 SIR Models LSTM
Committee Chair / Thesis Advisor	Lars Ruthotto, Emory University
Committee Members	Le Chen, Emory University Davide Fossati, Emory University

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