Control of a reaction-diffusion system: application on a SEIR epidemic mode

Abstract

In this work, we are interested in the study of a spatiotemporal SEIR epidemiological model, with no-flux boundary conditions. This model includes a constant inflow of new susceptible, exposed, infectious and recovered. In addition, it also incorporates a contact rate depending on the size of the population and another death related to the disease. Our objective is to characterize the optimal control pair, which minimizes exposed, infected individuals and the corresponding effort and treatment costs. We have demonstrated the existence of the state system solution and optimal control. The characterization of the optimal control pair is determined in terms of state functions and adjoint functions. The numerical resolution of the optimal system, has shown the effectiveness of our adopted strategy.