Optimal Control of SEIR Models for Disease Pandemics using Symplectic Euler Method

Abstract

This thesis focuses on disease modeling using single-group and multi-group SEIR models. The objective is to determine optimal control strategies. In order to apply optimal control strategies, a cost function is defined. An optimal control strategy leads to a decrease in cost. To solve the optimization problem, the Hamiltonian mechanics of the cost function are utilized. A constrained optimization problem is formulated, and the symplectic Euler method is employed to find a solution. The forward-backward sweep technique is then applied to maximize the Hamiltonian and minimize the cost, leading to the identification of optimal control strategies. A regularized version of the Hamiltonian is used to ensure convergence of the iteration process. Ultimately, a connection is established between the obtained optimal control strategy and its social interpretation.