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

• * Corresponding author

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.

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

 Citation: • • 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

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

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

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

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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