# American Institute of Mathematical Sciences

doi: 10.3934/cpaa.2021093

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

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

* Corresponding author

Received  December 2020 Revised  April 2021 Published  June 2021

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

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.

Citation: Hailiang Liu, Xuping Tian. Data-driven optimal control of a seir model for COVID-19. Communications on Pure & Applied Analysis, doi: 10.3934/cpaa.2021093
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(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
Scheduled control for the US in $270-300$ days by SEIR model
(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
(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
(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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