Three-Stage Numerical Solution for Optimal Control of COVID-19

Luis Vargas Tamayo, Vianney Mbazumutima, Christopher Thron and Léonard Todjihounde
Additional contact information
Luis Vargas Tamayo: Department of Sciences and Mathematics, Texas A & M University, CT, Killeen, TX 76549, USA
Vianney Mbazumutima: Institute of Mathematics and Physical Sciences, IMSP-Bénin, Abomey Calavi University, Porto-Novo B.P. 613, Benin
Christopher Thron: Department of Sciences and Mathematics, Texas A & M University, CT, Killeen, TX 76549, USA
Léonard Todjihounde: Institute of Mathematics and Physical Sciences, IMSP-Bénin, Abomey Calavi University, Porto-Novo B.P. 613, Benin

Mathematics, 2021, vol. 9, issue 15, 1-26

Abstract: In this paper, we present a three-stage algorithm for finding numerical solutions for optimal control problems. The algorithm first performs an exhaustive search through a discrete set of widely dispersed solutions which are representative of large subregions of the search space; then, it uses the search results to initialize a Monte Carlo process that searches quasi-randomly for a best solution; then, it finally uses a Newton-type iteration to converge to a solution that satisfies mathematical conditions of local optimality. We demonstrate our methodology on an epidemiological model of the coronavirus disease with testing and distancing controls applied over a period of 180 days to two different subpopulations (low-risk and high-risk), where model parameters are chosen to fit the city of Houston, Texas, USA. In order to enable the user to select his/her preferred trade-off between (number of deaths) and (herd immunity) outcomes, the objective function includes costs for deaths and non-immunity. Optimal strategies are estimated for a grid of (death cost) × (non-immunity cost) combinations, in order to obtain a Pareto curve that represents optimum trade-offs. The levels of the four controls for the different Pareto-optimal solutions over the 180-day period are visually represented and their characteristics discussed. Three different variants of the algorithm are run in order to determine the relative importance of the three stages in the optimization. Results from the three algorithm variants are fairly consistent, indicating that solutions are robust. Results also show that the Monte Carlo stage plays an especially prominent role in the optimization, but that all three stages of the process make significant contributions towards finding lower-cost, more effective control strategies.

Keywords: optimal control; testing; distancing; herd immunity; COVID-19; Monte Carlo; visualization; Pareto optimum (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/15/1777/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/15/1777/ (text/html)

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:gam:jmathe:v:9:y:2021:i:15:p:1777-:d:602400

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().