On the Regional Control of a Reaction-Diffusion System SIR.

This paper presents a study of regional optimal control strategies of a spatiotemporal SIR epidemic model which is formulated from existing SIR epidemic models by including a diffusion term. Our main objective is to characterize the two optimal controls that minimize the number of infected individuals, the corresponding vaccination and treatment costs. For that matter, we prove the existence of a pair of control and provide a characterization of optimal controls in terms of state and adjoint functions. Finally, we present numerical simulations on data concerning the evolution of the zoonotic Ebola virus in Africa. Results show that control is effective if regional treatment and vaccine strategies are used simultaneously.