Optimal control of a reaction–diffusion model related to the spread of COVID-19.

This paper is concerned with the well-posedness and optimal control problem of a reaction–diffusion system for an epidemic susceptible–exposed–infected–recovered–susceptible mathematical model in which the dynamics develops in a spatially heterogeneous environment. Using as control variables the transmission rates u e and u i of contagion resulting from the contact with both asymptomatic and symptomatic persons, respectively, we optimize the number of exposed and infected individuals at a final time T of the controlled evolution of the system. More precisely, we search for the optimal u i and u e such that the number of infected plus exposed does not exceed at the final time a threshold value Λ , fixed a priori. We prove here the existence of optimal controls in a proper functional framework and we derive the first-order necessary optimality conditions in terms of the adjoint variables. [ABSTRACT FROM AUTHOR]