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Collocation method with flood-based metaheuristic optimizer for optimal control ...
have their ways of spreading and hiding from handling large-scale, nonlinear systems or multi-
immune systems, showed how hard it is to con- objective problems. In addition, there are still
trol epidemics with more than one strain. These significant gaps in the research about improv-
changes are affected by competitive exclusion, in ing control strategies for multi-strain vaccination
which one strain beats out others, and coexis- programs. Specifically, many studies have not
tence, in which different strains can stay alive fully explored the role of strain amplification in
due to reinfection, cross-immunity, and muta- disease transmission, leaving this aspect largely
tion. The optimal control theory allows us to plan underexplored. Also, even though it is important
strategies, like immunizations, isolation, and pub- to find the best ways to control diseases, not many
lic awareness campaigns, that stop the spread of studies have looked at how to use computers to
disease as much as possible while considering the quickly solve these kinds of problems (called op-
cost and availability of healthcare. timal control problems, or OCPs) for multiple
strains of diseases. This study addresses these
Multi-strain epidemic mathematical models
challenges by proposing a hybrid framework inte-
build on single-strain frameworks like SIR and
grating a Laguerre-based collocation method with
SEIR by adding compartments and parameters
the flood-based metaheuristic optimizer (FBMO).
to account for how strains interact, how trans-
This method improves computation speed, deals
mission and recovery rates change, and how in-
with the complexity of multi-strain dynamics,
terventions affect different groups. These mod-
and looks into areas that have not been explored
els enable researchers to quantify the impact of
much, like strain amplification and the best way
control strategies and predict their outcomes un-
to vaccinate. By applying the proposed frame-
der different scenarios. Using optimal control on work to real-world COVID-19 data from Morocco,
these kinds of models lets us find the levels of in-
tervention (like vaccination rates or policies that we demonstrate its robustness and practical rele-
keep people from interacting with each other) vance for managing multi-strain epidemics effec-
tively. Therefore, the study adds to the knowl-
that minimize objective functions like the disease
edge about optimal control theory for epidemic
burden and the costs of intervention. Key ar-
models by looking into previously unexplored as-
eas of focus in these models include finding the
pects of strain amplification and improving vac-
best way to vaccinate so that limited resources
cination strategies. Another key objective is to
are used efficiently, finding the right balance be-
provide a computationally efficient approach for
tween isolation measures to stop the spread of
solving the OCP, which can enhance the precision
disease without causing too many social and eco-
and effectiveness of control measures in managing
nomic problems, and raising awareness about self-
the pandemic. The innovation also lies in utiliz-
protection to get more people to follow through ing Laguerre polynomials to transform the OCP
and lower the risk of getting sick. 4–6
into an NLP, making it computationally efficient
To better understand how COVID-19 and and providing better ways to handle multi-strain
its multi-strain variants move and behave, many pandemics like COVID-19.
mathematical models have been created to show The proposed methodology offers several key
how the epidemic spreads (see Table 1). We have benefits. The study ensures that the system’s dy-
employed these models to investigate the dynam- namics are accurately represented using the col-
ics of the pandemic and explore control measures, location method, making solving the OCP easier.
such as vaccination strategies, to mitigate its Adding the FBMO improves the global optimiza-
spread. Further research is still needed, though, tion, making it possible for the NLP to be solved
especially on the best ways to keep COVID-19 quickly. The practical application of this frame-
under control in vaccination programs, especially work to real-world COVID-19 data from Morocco
when it comes to multi-strain variants. This highlights its relevance and utility in optimiz-
study addresses this knowledge gap by compre- ing vaccination, isolation, and public awareness
hensively reviewing the current literature on opti- strategies. Therefore, this study helps move the
mal control strategies for COVID-19 multi-strain field forward by examining multi-strain epidemic
vaccination. control’s theoretical and practical sides and pro-
Even though there have been improvements, vides a valuable tool to address complex public
many studies that look at multi-strain epidemic health issues on a large scale.
control still use old-fashioned methods like the This paper’s orthogonal Laguerre collocation
Pontryagin Maximum Principle and Runge-Kutta method presents numerous benefits, including
methods. While effective in specific contexts, augmenting computational effectiveness, guaran-
these approaches often encounter difficulties in teeing precise solutions, improving efficiency and
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