A spatiotemporal SIR epidemic model two-dimensional with problem of optimal control. (English) Zbl 07801914
Summary: In the context of a more realistic model, in this work, we are interested in studying a spatiotemporal two-dimensional SIR epidemic model, in the form of a system of partial differential equations (PDE). A distribution of a vaccine in the form of a control variable is considered to force immunity. The purpose is to characterize a control that minimizes the number of susceptible, infected individuals and the costs associated with vaccination over a finite space and time domain. In addition, the existence of the solution of the state system and the optimal control is proved. The characterization of the control is given in terms of state function and adjoint function. The numerical resolution of the state system shows the effectiveness of our control strategy.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35L70 | Second-order nonlinear hyperbolic equations |
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