Abstract
In this paper, an SIR spatiotemporal epidemic model is formulated as a system of parabolic partial differential equations with no-flux boundary conditions. Immunity is forced through vaccine distribution considered a control variable. Our principal objective is to characterize an optimal control that minimizes the number of infected individuals and the costs associated with vaccination over a finite space and time domain. The existence of solutions to the state system and the existence of an optimal control is proved. An optimal control characterization in terms of state and adjoint functions is provided. Furthermore, a second condition of optimality is given. The optimality systems are solved based on an iterative discrete scheme that converges following an appropriate test similar the one related to the forward–backward sweep method. Numerical results are provided to illustrate the effectiveness of our approach for several scenarios.
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