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

  • * Corresponding author

    * Corresponding author 

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

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  • 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:

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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

    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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