Optimal Regional Control of a Time-Fractional Spatiotemporal SIR Model with Vaccination and Treatment Strategies

In this study, we analyze a time-fractional spatiotemporal SIR model in a specific area Ω. Taking into account the available resources, vaccines are allocated to region ω1⊆Ω and treatments to region ω2⊆Ω, which may or may not coincide. Our objective is to minimize infections and costs by implementing an optimal regional control strategy. We establish the existence of optimal controls and related solutions, providing a characterization of optimal control in terms of state and adjoint functions. We employ the forward–backward sweep method to solve the associated optimality system numerically. The findings indicate that a combined strategy of vaccination and treatment is more effective in reducing disease transmission from adjacent regions.