Data-driven optimal control of a seir model for COVID-19

Hailiang Liu; Xuping Tian

doi:10.3934/cpaa.2021093

Article Contents

2023, Volume 22, Issue 1: 19-39. Doi: 10.3934/cpaa.2021093

This issue Previous Article Analysis of COVID-19 epidemic transmission trend based on a time-delayed dynamic model Next Article A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion

Data-driven optimal control of a seir model for COVID-19

Hailiang Liu^1, , and
Xuping Tian^2,

1.
Department of Mathematics, Iowa State University, Ames, IA 50011, USA
2.
Department of Mathematics, Iowa State University, Ames, IA 50011, USA

^* Corresponding author
^* Corresponding author

Received: December 2020

Revised: April 2021

Early access: June 2021

Published: January 2023

This research was supported by the National Science Foundation under Grant DMS1812666

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Abstract

We present a data-driven optimal control approach which integrates the reported partial data with the epidemic dynamics for COVID-19. We use a basic Susceptible-Exposed-Infectious-Recovered (SEIR) model, the model parameters are time-varying and learned from the data. This approach serves to forecast the evolution of the outbreak over a relatively short time period and provide scheduled controls of the epidemic. We provide efficient numerical algorithms based on a generalized Pontryagin's Maximum Principle associated with the optimal control theory. Numerical experiments demonstrate the effective performance of the proposed model and its numerical approximations.

Keywords:

Mathematics Subject Classification: Primary: 34H05, 92D30; Secondary: 49M05, 49M25.

Citation:

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Figure 1. (a) Reported and fitted cumulative infection and death cases in the US (b) Estimated SEIR parameters and the basic reproduction number. $ \beta $ ($ \mu $) corresponds to the left (right) vertical axis, $ \epsilon = 0.2 $ and $ \gamma = 0.1 $ are almost constant. The dashed line in $ R_0 $ is a zoomed-in version on the tail of the solid line

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Figure 2. Scheduled control for the US in $ 270-300 $ days by SEIR model

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Figure 3. (a) Reported and fitted cumulative infection and death cases in the UK (b) Estimated SEIR parameters and the basic reproduction number. $ \beta $ ($ \mu $) corresponds to the left (right) vertical axis, $ \epsilon = 0.2 $ and $ \gamma = 0.1 $ are almost constant. The dashed line in $ R_0 $ is a zoomed-in version on the tail of the solid line

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Figure 4. (a) Reported and fitted cumulative infection and death cases in France (b) Estimated SEIR parameters and the basic reproduction number. $ \beta $ ($ \mu $) corresponds to the left (right) vertical axis, $ \epsilon = 0.2 $ and $ \gamma = 0.1 $ are almost constant. The dashed line in $ R_0 $ is a zoomed-in version on the tail of the solid line

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Figure 5. (a) Reported and fitted cumulative infection and death cases in China (b) Estimated SEIR parameters and the basic reproduction number. $ \beta $ ($ \mu $) corresponds to the left (right) vertical axis, $ \epsilon = 0.2 $ and $ \gamma = 0.2 $ are almost constant. The dashed line in $ R_0 $ is a zoomed-in version on the tail of the solid line

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