The flowchart presents a detailed flow of process and information as a build-up from the procedure described above.
The detailing shows the various levels of initialization and conditional checking. Also, the computation leading to the
exploration and exploitation stages of the proposed EOSA metaheuristic algorithm is detailed. Also, the procedure for
update all subgroups are also identified. In the following subsection, the mathematical model applies to the flowchart
of the algorithm presented and discussed.
3.3 Mathematical Model of EOSA
As earlier noted, we represent SEIR-HDVQ in this paper base on the definition of Susceptible (S), Infected (I),
Hospitalized (H), Exposed (E), Recovered (R), Funeral (F), Dead (D), Vaccination (V), and Quarantine (Q). To update
the positions of each exposed individual, Equation 1 applies:
where ρ represents the scale factor of displacement such individuals,
and
are respectively the updated and
original position at time t, and t+1 is the current time. M(I) is the movement rate made by individuals, which is further
defined thus:
The exploitation stage of the EOSA optimization algorithm assumes that the infected individual either stays within a
distance of zero (0), or is displaced within a limit not exceeding srate denoting short distance movement. The
exploration phase of the algorithm assumes that the infected individual has moved beyond the normal neighborhood
range lrate. The consideration in this study is that the farther the displacement, the more the number of contacts
exposed to the infection. Equations 2 and 3, therefore, ensure that the movement of each individual in consideration
is appropriately assigned. Both srate and lrate are regulated by neighborhood parameter. If neighborhood is over 0.5,
we assume the individual has moved beyond the neighborhood otherwise, remains within the neighborhood.
Initialization of Susceptible population: At the beginning, an initial population is generated by means of random
number distribution whose initial positions are all zero (0), so that i
th
individual is generated as shown in Equation 4.
The function rand (0, 1) generates uniformly distributed values, the variable i, and U
i
and L
i
denote the upper and
lower bounds respectively for the i
th
individual, ranges from 1,2,3…. N, where is the population size.
The selection of the current best is carried out on the set of infected individuals in time t. meanwhile, the selection of
the global best is based on the following:
where bestS, gBest and cBest all denotes the best solution, global best solution, and current best solution at time t;
fitness(.) represents the objective function applied to the problem. We distinguish gBest and cBest as infected
individuals who Superspreader and Spreader of the Ebola virus, respectively.
Update of Susceptible (S), Infected (I), Hospitalized (H), Exposed (E), Vaccinated (V), Recovered (R), Funeral (F),
Quarantine (Q), and dead (D) uses a system of ordinary differential equations based on those in (Berge, Lubuma,
Moremedi, Morris, & Kondera-Shava, 2017) (Tanade, Pate, Paljug, Hoffman, & Wang, 2019). Differential calculus
is a branch of calculus that is a branch in mathematics, where the former deals with the rate of change of one quantity
concerning another, while the latter deals with finding different properties of integrals and derivatives. The application