Page 101 - IJOCTA-15-2

A. Ebrahimzadeh, R. Khanduzi, A. Jajarmi / IJOCTA, Vol.15, No.2, pp.294-310 (2025)
Table 1. Categorization of pertinent studies on multi-strain COVID-19 models published in the literature

Paper Model Data Solution Approach Vaccination Multi-Strain
[9] SEIQRDV Saudi Arabia Ensemble Kalman Filter ✓ ✗
[10] SEIQR Pakistan Pontryagin’s Maximum Principle ✗ ✗
[11] SEIARQD Nigeria Pontryagin Maximum Principle ✗ ✗
[12] SS q EIQAHR Malaysia Fourth Order Runge-Kutta Method ✗ ✗
[13] SIR China Runge-Kutta-Fehlberg method ✓ ✗
[14] SVEIR Pakistan Pontryagin Maximum Principle ✓ ✗
[15] SEAIR Pakistan Forward-backward Runge-Kutta method ✓ ✗
[17] SEVI u I I R u R k India Pontryagin Maximum Principle ✓ ✗
[18] SEIR England Pontryagin Maximum Principle ✓ ✓
[19] SIR Unknown Pontryagin Maximum Principle ✓ ✓
[20] SVI s I v R Morocco Pontryagin Maximum Principle ✓ ✓
[21] SIR Unknown Stochastic Maximum Principle ✓ ✓
[22] SLIHQR UK Pontryagin Maximum Principle ✓ ✓
[23] SEAIGRD India Pontryagin Maximum Principle ✓ ✓
Current Paper SVI c I v R Morocco Collocation method and FBMO ✓ ✓

numerical accuracy, and facilitating straightfor- of the local approaches used to solve large-scale
ward implementation when addressing complex nonlinear optimization problems because they are
systems. Alternatively, the sparse derivative op- efficient. 24–26 However, they get local solutions in
erational matrix approximates the derivative La- a high running time as the problem dimension in-
guerre vector, significantly boosting the compu- creases. To prevent these types of defects, a meta-
tational process’s reliability and efficiency. The heuristic algorithm called FBMO is developed in
rationale behind selecting Laguerre polynomials this paper. The efficacy of FBMO in making
as a basis for the approximations is as follows: high decisions and global searches are some of
1- Laguerre polynomials are orthogonal con- the benefits of using FBMO to solve the con-
cerning the exponential weight function verted OCP of the multi-strain COVID-19 model
−t
ω(t) = e , which naturally aligns with in the form of an NLP. More to the point, the
problems involving decaying processes FBMO is among the newly published prosperous
over time. This property ensures sta- metaheuristic methods that attracted the inter-
bility and precision in approximating our est of various authors in this short period of one
27–32
model’s state and control variables. year. Indeed, the FBMO is a nature-inspired
2- Expanding functions in terms of Laguerre optimization method that simulates the regular
polynomials facilitates the reduction of movement and flow processes of water masses
the infinite-dimensional OCP to a finite- throughout the flooding phenomenon in nature.
dimensional system. This significantly It obtains near-optimal answers or the global
reduces computational complexity while minimum of NLPs efficiently. About the novel
preserving high accuracy. FBMO, it should be noted that this approach
is efficient and robust, significantly when solving
3- Laguerre polynomials have sparse deriva- 27
tive operational matrices, which makes it large-sized instances of NLPs. Comparing the
easier to solve the NLP that comes from FBMO algorithm with some recent metaheuristic
the OCP. methods is a noteworthy comparison, after which
4- Several OCPs have been successfully the performance of the FBMO is well-appraised
solved using Laguerre-based collocation compared to benchmark functions and engineer-
27–32
methods. This shows that they work well ing problems. The assessment of the FBMO’s
and are reliable when using computers results assimilates four statistical metrics: mean,
to deal with constraints and dynamics in best, standard deviation, and average Friedman
complex systems. rank. These values are considered for ranking the
metaheuristic methods concerning each bench-
Because of these features, Laguerre polynomi-
mark function and engineering problem. These
als were chosen as the best way to turn the OCP of
criteria show that the FBMO provided highly
the multi-strain COVID-19 model into a solvable
competitive solutions compared to some modern
NLP. This facilitated the rapid and accurate iden- metaheuristic methods. 27–32 Therefore, we have
tification of the most effective control strategies.
proven that the FBMO is a suitable approach for
Since the converted OCP for the multi-strain
our NLP problem.
COVID-19 is a large-scale NLP, we should select
efficient local and metaheuristic methods to solve The proposed hybrid strategy, combining the
this optimization problem. Conjugate gradient, collocation method with the FBMO, offers several
trust-region, and quasi-Newton methods are some key advantages:
296