Optimal Control of an Epidemic with Intervention Design

Abstract: In this paper, I propose a controlled SEIR model that advances epidemic management through optimal control theory. I improve the traditional framework by incorporating practical intervention constraints and economic considerations. Approaching this problem using modern methods of calculus of variations, I first conduct a rigorous mathematical analysis of the controlled system. Then, I formulate an infinite time horizon control problem and investigate its mathematical connections with finite time, setting the stage for applying the Hamiltonian procedure.