# Load Forecasting Based on LVMD-DBFCM Load Curve Clustering and the CNN-IVIA-BLSTM Model
## 2 Influenza Virus Immunity Optimization Algorithm
### Mathematical Model  
The process of influenza virus transmission in a population is mapped with the influenza virus immunization algorithm. The population is represented by the matrix \(X\), as shown in Equation (1), where \(n\) is the population size and the number of individuals, and \(d\) is the number of cells invaded by the influenza virus into the human body, corresponding to the dimensionality of the objective function. The initialization process of the algorithm randomly generates an \(n\times d\) dimension matrix \(X\), which sets the initial number of infected individuals to \(x\). \[X= \begin{bmatrix}x_{11}&x_{12}&\cdots&x_{1d}\\ x_{21}&x_{22}&\cdots&x_{2d}\\ \vdots&\vdots&\ddots&\vdots\\ x_{n1}&x_{n2}&\cdots&x_{nd}\end{bmatrix}  \tag{1}\]  
The fitness values of different individuals in the population are represented by Equation (2). Each row in the matrix is represented as the fitness value of the current individual. The individual corresponding to the optimal fitness value is the current optimal solution of the objective function. \[F(x)= \begin{bmatrix}f(x_{11},\ x_{12},\cdots,\ x_{1d})\\ f(x_{21},\ x_{22},\cdots,\ x_{2d})\\ \vdots\\ f(x_{n1},\ x_{n2},\cdots,\ x_{nd})\end{bmatrix}  \tag{2}\]  
The distance between individuals is represented by \(C\), as shown in Equation (3). \(x=\{x_{1},\ x_{2},\ \ldots,\ x_{d}\}\) is the position of individual \(x\), \(y=\{y_{1},\ y_{2},\ldots,\ y_{d}\}\) is the position of individual \(y\), and \(d\) is the dimension of the optimization problem. \[C=\sqrt{\left(x_{1}-y_{1}\right)^{2}+\left(x_{2}-y_{2}\right)^{2}+\ldots+\left( x_{d}-y_{d}\right)^{2}} \tag{3}\]  
\(L\) is the maximum safety distance, as shown in Equation (4). \(\left(L_{\min},\ L_{\max}\right)\) represents the range of values for individuals. \[L=\frac{1}{2}\sqrt{L_{\min}^{2}+L_{\max}^{2}} \tag{4}\]  
The virus spreading process corresponds to the iterative optimization-seeking process in the algorithm. It is assumed that the safe distance between other individuals and the  
Figure 4: Growth curve of the number of infected people. infected person when the influenza virus spreads in the population is \(L\). The iterative formulas for individuals in different cases are shown in Equations (5) to (9). * Infected individuals are updated by Equation (5): \[x_{i,j}(t+1)=x_{i,j}(t)\left(\exp\left(\frac{N_{\max}-n}{N_{\max}}-1\right)\times \frac{1}{d-1}\right)^{q}\] (5)  
When the contact distance between individuals in the population and infected individuals is \(C<0.2L\), the individuals are moved into the infected state. The position of infected individuals is updated by Equation (5). \(N_{\max}\) is the maximum number of iterations, \(n\) is the current number of iterations, \(d\) is the dimensionality of the optimization problem, and \(q\) is used to regulate the individual position update rate. The larger the value is of \(q\), the faster the position update rate and the higher the accuracy of the optimization search. * Extremely susceptible individuals are updated by Equation (6): \[x_{i,j}(t+1) =x_{i,j}(t)+\alpha\big{|}x_{i,j}(t)-x_{i,q}(t)\big{|}\] \[\alpha =\frac{1}{d}\sum\limits_{p=1}^{d}rand(-1,1)\] (6)  
When the contact distance between individuals in the population and infected individuals is \(0.2L<C<0.5L\), the position is updated by Equation (6). \(x_{i,q}(t)\) is the random acquisition of viral cells by highly susceptible individuals; \(\alpha\) represents update coefficient at the contact distance of \(0.2L<C<0.5L\). When the number of exchanged cells exceeds a quarter of the total number of cells, the highly susceptible individuals are transformed into infected individuals. Cell exchange occurs only once during each iteration, and the number of exchanges is random.