Reliable optimal controls for SEIR models in epidemiology

Simone Cacace and Alessio Oliviero

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 223, issue C, 523-542

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.

Keywords: Optimal control; SEIR model; Dynamic programming; Hamilton–Jacobi; Pontryagin maximum principle; Direct-adjoint looping (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475424001605
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:223:y:2024:i:c:p:523-542

DOI: 10.1016/j.matcom.2024.04.034

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().