Reliable optimal controls for SEIR models in epidemiology

TL;DR

This paper compares two optimal control methods for SEIR epidemiological models, proposing a combined approach to improve solution reliability and applying it to simulate epidemic control policies.

Contribution

It introduces a combined control strategy using Dynamic Programming and Pontryagin's maximum principle for more reliable epidemic management solutions.

Findings

The combined method yields high-quality control policies.

Simulations demonstrate effective epidemic spread mitigation.

First and second order optimality conditions validate solutions.

Abstract

We present and compare two different optimal control approaches applied to SEIR models in epidemiology, which allow us to obtain some policies for controlling the spread of an epidemic. The first approach uses Dynamic Programming to characterise the value function of the problem as the solution of a partial differential equation, the Hamilton-Jacobi-Bellman equation, and derive the optimal policy in feedback form. The second is based on Pontryagin's maximum principle and directly gives open-loop controls, via the solution of an optimality system of ordinary differential equations. This method, however, may not converge to the optimal solution. We propose a combination of the two methods in order to obtain high-quality and reliable solutions. Several simulations are presented and discussed, also checking first and second order necessary optimality conditions for the corresponding numerical solutions.