## 3 System Model
### Model Building
\begin{array}{ccc}\left(\begin{array}{ccc}0&0&0\\ 0&s_{2}\hat{p}_{1}(\hat{p}_{2}+p_{2}\frac{m}{a})&0\\ 0&s_{1}\hat{p}_{1}(\hat{p}_{2}+p_{2}\frac{m}{a})&0\end{array}\right)_{2\times 3 }&m\leq H\\ \\ \left(\begin{array}{cc}0&s_{2}\hat{p}_{1}(\hat{p}_{2}+p_{2}\frac{m}{a})&0\\ 0&s_{1}\hat{p}_{1}(\hat{p}_{2}+p_{2}\frac{m}{a})&0\end{array}\right)_{2\times 3 }&m\!\!=\!\!H+1\\ \\ \left(\begin{array}{cc}s_{2}\hat{p}_{1}(\hat{p}_{2}+p_{2}\frac{m}{a})&0\\ s_{1}\hat{p}_{1}(\hat{p}_{2}+p_{2}\frac{m}{a})&0\end{array}\right)_{2\times 2 }&m\geq H+2\end{array} \right.\] (9)
4. When \(1\leq m\leq K\) and \(n=m\), \(W_{m,n}\) is expressed as follows. \[W_{m,n}=\left\{ \begin{array}{ccc}\left(\begin{array}{cc}\hat{p}_{1}(\hat{p} _{2}+p_{2}\frac{m}{a})&0&0\\ 0&s_{2}\hat{p}_{1}p_{2}(1-\frac{m}{a})+s_{2}\hat{p}_{1}(\hat{p}_{2}+p_{2}\frac{ m}{a})&s_{2}\hat{p}_{1}(\hat{p}_{2}+p_{2}\frac{m}{a})\\ 0&s_{1}\hat{p}_{1}p_{2}(1-\frac{m}{a})&(s_{1}\hat{p}_{1}+\hat{s}_{1})(\hat{p}_{ 2}+p_{2}\frac{m}{a})\end{array}\right)_{3\times 3}&m\leq H\\ \\ \left(\begin{array}{cc}s_{2}\hat{p}_{1}p_{2}(1-\frac{m}{a})+s_{2}\hat{p}_{1} (\hat{p}_{2}+p_{2}\frac{m}{a})&s_{2}\hat{p}_{1}(\hat{p}_{2}+p_{2}\frac{m}{a}) \\ s_{1}\hat{p}_{1}p_{2}(1-\frac{m}{a})&(s_{1}\hat{p}_{1}+s_{1})(\hat{p}_{2}+p_{2} \frac{m}{a})\end{array}\right)_{2\times 2}&m\geq H+1\end{array} \right.\] (10)When \(1\leq m\leq K-1\) and \(n=m+1\), \(\mathbf{W}_{m,n}\) is expressed as follows. \[\mathbf{W}_{m,n}=\left\{ \begin{array}{cc}\left(\begin{array}{cc}\tilde{p}_{1}p_{2 }(1-\frac{m}{\alpha})&0&p_{1}(\tilde{p}_{2}+p_{2}\frac{m}{\alpha})\\ 0&s_{2}\tilde{p}_{1}p_{2}(1-\frac{m}{\alpha})&s_{2}p_{1}(\tilde{p}_{2}+p_{2} \frac{m}{\alpha})+s_{2}p_{1}p_{2}(1-\frac{m}{\alpha})\\ 0&0&(s_{1}p_{1}+\tilde{s}_{1})p_{2}(1-\frac{m}{\alpha})\end{array}\right)_{3 \times 3}&m\leq H-1\\ \\ \left(\begin{array}{cc}\tilde{p}_{1}p_{2}(1-\frac{m}{\alpha})&p_{1}(\tilde{p} _{2}+p_{2}\frac{m}{\alpha})\\ s_{2}p_{1}p_{2}(1-\frac{m}{\alpha})&s_{2}p_{1}(\tilde{p}_{2}+p_{2}\frac{m}{ \alpha})+s_{2}p_{1}p_{2}(1-\frac{m}{\alpha})\\ 0&(s_{1}p_{1}+\tilde{s}_{1})p_{2}(1-\frac{m}{\alpha})\end{array}\right)_{3 \times 2}&m=H\\ \\ \left(\begin{array}{cc}s_{2}\tilde{p}_{1}p_{2}(1-\frac{m}{\alpha})&s_{2}p_{1 }(\tilde{p}_{2}+p_{2}\frac{m}{\alpha})+s_{2}p_{1}p_{2}(1-\frac{m}{\alpha})\\ 0&(s_{1}p_{1}+\tilde{s}_{1})p_{2}(1-\frac{m}{\alpha})\end{array}\right)_{2 \times 2}&m\geq H+1\\ \\ \left(\begin{array}{cc}\tilde{s}_{2}\tilde{p}_{1}p_{2}(1-\frac{m}{\alpha})& \tilde{s}_{2}p_{1}+s_{2}p_{1}p_{2}(1-\frac{m}{\alpha})\\ 0&(s_{1}p_{1}+\tilde{s}_{1})p_{2}(1-\frac{m}{\alpha})\end{array}\right)_{2 \times 2}&m\geq H+1\\ \\ \end{array} \right. \tag{11}\]  
When \(m=K\) and \(n=m+1\), \(\mathbf{W}_{m,n}\) is expressed as follows. \[\mathbf{W}_{m,n}=\left\{ \begin{array}{cc}\left(\begin{array}{cc}\tilde{p}_{1}p _{2}(1-\frac{m}{\alpha})&p_{1}\\ \tilde{s}_{2}p_{1}p_{2}(1-\frac{m}{\alpha})&s_{2}p_{1}+s_{2}p_{1}p_{2}(1-\frac {m}{\alpha})\\ 0&(s_{1}p_{1}+\tilde{s}_{1})p_{2}(1-\frac{m}{\alpha})\end{array}\right)_{3 \times 2}&m=H\\ \\ \left(\begin{array}{cc}\tilde{s}_{2}\tilde{p}_{1}p_{2}(1-\frac{m}{\alpha})& \tilde{s}_{2}p_{1}+s_{2}p_{1}p_{2}(1-\frac{m}{\alpha})\\ 0&(s_{1}p_{1}+\tilde{s}_{1})p_{2}(1-\frac{m}{\alpha})\end{array}\right)_{2 \times 2}&m\geq H+1\\ \\ \end{array} \right. \tag{12}\]  
When \(m=K\) and \(n=m+2\), \(\mathbf{W}_{m,n}\) is expressed as follows. \[\mathbf{W}_{m,n}=\left\{ \begin{array}{cc}\left(\begin{array}{cc}0&s_{2}\tilde{ p}_{1}(\tilde{p}_{2}+p_{2}\frac{K+1}{\alpha})&0\\ 0&s_{1}\tilde{p}_{1}(\tilde{p}_{2}+p_{2}\frac{K+1}{\alpha})&0\end{array}\right)_ {2\times 3}&m=H+1\\ \\ \left(\begin{array}{cc}s_{2}\tilde{p}_{1}(\tilde{p}_{2}+p_{2}\frac{K+1}{ \alpha})&0\\ s_{1}\tilde{p}_{1}(\tilde{p}_{2}+p_{2}\frac{K+1}{\alpha})&0\end{array}\right)_ {2\times 2}&m\geq H+2\\ \\ \end{array} \right. \tag{13}\]  
When \(m=K+1\) and \(n=m-1(n\
eq 0)\), \(\mathbf{W}_{m,n}\) is expressed as follows. \[\mathbf{W}_{m,n}=\left\{