Page 99 - IJOCTA-15-2

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.2, pp.294-310 (2025)
https://doi.org/10.36922/ijocta.1735

RESEARCH ARTICLE

Collocation method with flood-based metaheuristic optimizer for
optimal control on a multi-strain COVID-19 model

2*
1
Asiyeh Ebrahimzadeh , Raheleh Khanduzi , and Amin Jajarmi 3,4*
1
Department of Mathematics Education, Farhangian University, P.O. Box, 14665-889, Tehran, Iran
2
Department of Mathematics and Statistics, Gonbad Kavous University, P. O. Box, 49771-99151, Gonbad
Kavous, Iran
3
Department of Electrical Engineering, University of Bojnord, P.O. Box, 94531-1339, Bojnord, Iran
4
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical
Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India
a.ebrahimzadeh@cfu.ac.ir, khanduzi@gonbad.ac.ir, a.jajarmi@ub.ac.ir
ARTICLE INFO ABSTRACT

Article History: This paper describes a new and powerful way to solve optimal control problems
Received: November 17, 2024 (OCPs) on a multi-strain COVID-19 model for strategies related to vaccina-
Accepted: February 19, 2025 tion and amplification. We call it the collocation method with a flood-based
Published Online: April 4, 2025 metaheuristic optimizer (FBMO). We use a collocation method with Laguerre
Keywords: polynomials and their derivative operational matrices to turn the OCP into
Multi-strain a nonlinear programming (NLP) problem. To address the NLP, the research
Amplification employs the FBMO to determine the control variables u i for i = 1, 2, and 3,
Optimal control representing isolation, vaccination efficacy, and treatment enhancement, in con-
Vaccination junction with the state function of the multi-strain COVID-19 model. These
Collocation method strategies are executed within an SVI cI vR-type control model for COVID-19 in
Flood-based metaheuristic optimizer Morocco, designed to control the outbreak of multi-strain disease. The paper’s
primary aim is to achieve a high-quality optimal solution for the given OCP,
AMS Classification:
thereby contributing to the advancement of efficient strategies for managing
49J21; 65N35; 97R40
the COVID-19 pandemic.

1. Introduction and background strains can stay alive in the coexistence scenario.
These include viral mutations that create new
The Omicron variant of COVID-19 has caused strains, reinfection with different strains, mixed
much worry worldwide because it has many mu- infections, cross-immunity between strains, mor-
tations and is very good at hiding from the im- tality rates that depend on density, exponential
mune system compared to other variants. Two growth dynamics, and vaccinations that change
main types of dynamics can explain how multi- the competitive landscape. For example, in the
strain infectious diseases like COVID-19 spread: case of COVID-19, the Omicron variant and its
1
competitive exclusion and coexistence. The com- subvariants spread quickly because they were bet-
petitive exclusion scenario says that when differ- ter at hiding from the immune system. This
ent strains compete within the same host pop- meant that they had the ability to infect indi-
ulation, the strain with the highest basic repro- viduals who had already received vaccinations or
duction number (R 0 )–the strain that can spread contracted the disease. Due to its immunity and
the most–will win and replace the other strains. ease of spread, Omicron defeated earlier versions
Researchers have developed various mathematical and took their place in various locations. 2,3
models to simulate the progression of multi-strain
infectious diseases, including COVID-19. These The COVID-19 pandemic underscored the
models have primarily focused on exploring con- critical need for effective control strategies to
trol measures, such as vaccination and isolation manage the spread of multi-strain infectious dis-
strategies. There are many reasons why different eases. Variants like Delta and Omicron, which
*Corresponding Author
294