Page 103 - IJOCTA-15-2

A. Ebrahimzadeh, R. Khanduzi, A. Jajarmi / IJOCTA, Vol.15, No.2, pp.294-310 (2025)
Table 2. Model parameters and their definitions

Parameter Definition
Λ Recruitment rate of susceptible population
µ Natural mortality rate
β Effective contact rate between infected and susceptible populations
c c Death rate due to common strain infection
c v Death rate due to amplified strain infection
Cure rate of infected population with amplified strain
w v
w c Cure rate of infected population with common strain
ρ Proportion of individuals transitionary from common strain to amplified strain
α Inhibition or psychological factor in population behavior
ψ Vaccination rate

Table 3. Model variables and their definitions

State variable Definition
N Total available population
S Susceptible people
V Vaccinated people
Infected population with drug-sensitive strain at time t
I v
I c Number of infected population with common strain at time t
R Recovered people
Control variable Definition
u 1 Change in vaccination strategy
u 2 Effectiveness of isolation for I v
u 3 Increase of awareness of self-protection for the infected population I c under media coverage

so u 2 (t) signifies the efficacy of isolation for I v ,
while u 3 (t) represents the enhancement of self- min J(u 1 , u 2 , u 3 ) =
protection awareness among the infected popula- Z T
1
2
2
2
2
tion I c due to media coverage. Subsequently, we B 1 I + B 2 I + B 3 u + B4u + B5u 2 dt,
c
3
2
1
v
2
present the control model as follows: 0
(11)
in which the state functions I c and I v , as well as
the control functions u i for i = 1, 2, 3, are bal-
dS anced by parameters B i for i = 1, 2, 3, 4, 5 with
=Λ − u 1 (t)S − µS − (1 − u 2 )βSI v
dt the final time denoted as T. This optimization
process involves determining the optimal values
βS(1 − u 3 (t))I c
− , (6) of u as outlined in Table 3.
1 + αI c i
dV
= − (1 − u 2 (t))βI v V − µV + u 1 (t)S, (7) 3. Solution approach
dt
dI c The section introduces a novel hybrid strategy
= − (µ + c c + ρw c + (1 − ρ)w c )I c
dt to address the OCP related to a multi-strain
β(1 − u 3 (t))SI c COVID-19 model. The method for solving the
+ , (8)
1 + αI c OCP involves key steps. At first, it shows how
the basic features of Laguerre polynomials and
dI v
=β(1 − u 2 (t))I v V + β(1 − u 2 (t))SI v the derivative operational matrices that go with
dt
+ (1 − ρ)w c I c − (µ + c v + w v )I v , (9) them are important parts of the method. The
Laguerre-based collocation technique then breaks
dR
= − µR + w v I v + ρw c I c . (10) down the OCP into an NLP problem. This trans-
dt
formation allows for leveraging the advantages of
the collocation technique in handling dynamical
constraints and converting the OCP into a more
tractable form. Finally, a novel metaheuristic al-
The objective function to be minimized is de- gorithm called FBMO addresses the NLP and de-
fined as: termines the optimal solution for the OCP. This
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