## 4 Proposed Methodology
### Cluster Head Selection
#### 4.1.2 Ebola Optimization Search Algorithm (EOSA)  
This section represents the different stages of the condition checking and initialization process [30]. The computation process leading to the investigation and utilization of the EOSA algorithm is shown and the subgroup's updated procedures are determined. The below equation which describes updating the positions of the individual is expressed as,  
\[M_{j}^{T+1}=M_{j}^{T}+\alpha N(i) \tag{8}\]  
where \(\alpha\), \(N(i)\) represents the scale factor and movement rate, respectively. \(M_{i}^{T}\), \(M_{j}^{T+1}\) are the original and updated positions. The movement rate is defined as,  
\[N(i)=SRate*Rand(0,1)+N(ind_{Best}) \tag{9}\]  
\[N(S)=LRate*Rand(0,1)+N(ind_{Best}) \tag{10}\]  
The term \(SRate\) implies short-distance movement. The investigation stage is used to find the impact when the infected individual shifts beyond the range of \(LRate\). The \(LRate\) and \(SRate\) are arranged by using neighborhood parameters.  
Initializing the susceptible populations  
Initially, the initial populations are generated by using a random value of distributions along with zero position. The generation of individuals is shown in the below equation,  
\[individual_{j}=l_{j}+Rand(0,1)*\left(u_{j}+l_{j}\right) \tag{11}\]  
where,\(u_{j}\), \(l_{j}\) signifies both upper and lower boundaries, respectively. \(i\) represents the values from \(1,\ 2,\ 3,\ \ldots\ldots,\ n\). The combination of best solution selection and infected individuals are shown in the below equation,  
\[BestD=\left\{\begin{array}{l}G\ best,\ \ Fitness(C\ best)< Fitness(G\ best)\\ C\ best,\ \ Fitness(C\ best)\geq Fitness(G\ best)\end{array}\right. \tag{12}\]  
Here, \(BestD\), \(G\ best\), \(C\ best\) represents the best solutions, global best solutions, and current best solutions respectively. \(G\ best\), \(C\ best\) denote super-spreader and transmitter, respectively.  
The vaccinated \((v)\), infected \((i)\), exposed \((e)\), susceptible \((D)\), hospitalized \((h)\), quarantine \((q)\), funeral \((f)\), dead \((d)\), and recovered \((r)\) are used in the differential calculus and is shown below,  
\[\frac{\partial D(T)}{\partial T}=\pi-\left(\eta_{1}\ i+\eta_{3}\ d+\eta_{4}\ r+\eta_{2}\ (pe)\right)\ D-\left(\phi\ D+\phi\ i\right) \tag{13}\]  
\[\frac{\partial i(T)}{\partial T}=\left(\eta_{1}\ i+\eta_{3}\ d+\eta_{4}\ r+\eta_{2}\ (pe)\ \psi\right)\ D-\left(\phi+\theta\right)\ i-\left(\phi\right)\ D \tag{14}\]  
\[\frac{\partial h(T)}{\partial T}=\beta\ i-\left(\theta+\mu\right)\ h \tag{15}\]\[\frac{\partial r(T)}{\partial T}=\theta\,i-\varphi\,r \tag{16}\]  
\[\frac{\partial v(T)}{\partial T}=\theta\,i-(\lambda+\sigma)\,v \tag{17}\]  
\[\frac{\partial d(T)}{\partial T}=(\phi\,D+\varphi\,i)-\tau\,d \tag{18}\]  
\[\frac{\partial q(T)}{\partial T}=(\pi\,i-(\theta\,\ r+\varphi\,d))-\omega\,q \tag{19}\]  
The above-mentioned equations are denoted as a scalar function which has one value; that value is represented as a float. The exponential growth is described by using a scalar differential equation:  
\[k^{\prime}=\vartheta\,k \tag{20}\]  
where, \(k\) implies the growth rate.