## 4 Numerical Example
The WC performance of the SMs is shown in Figure 11. The detailed calculation data are listed in Table 5. It can first be seen from Figure 11b that, throughout the whole process, there is little difference in the number of valid waked SMs between the two methods. However, it can be clearly seen from Figure 11a that the number of waked SMs via the BDIIM method is fewer than that achieved via the DIDM method throughout the whole process, especially after 20 s. The ratio of the number of valid waked SMs to the total number of waked SMs is given in Figure 11c. The average ratio via the proposed method in this work approaches 0.38, while the average ratio via the previous method is about 0.25 during this period. Compared with the previous method, the ratio is improved by approximately 52% by using the proposed method. Furthermore, the ratio of the number of valid waked SMs to the idle number of waked SMs, shown in Figure 11d, demonstrates that the wake efficiency of SMs via the BDIIM method is higher than that achieved via the DIDM method. Figure 5: The state of the sensing module (SM) at the 10 th time interval. Figure 6: The state of the SM at the 20 th time interval. Figure 7: The state of the SM at the 30 th time interval. Figure 8: The state of the communication module (CM) at the 10 th time interval. Figure 9: The state of the CM at the 20 th time interval. Figure 11: The WC performance of SMs: (**a**) Number of waked SMs. (**b**) Number of valid waked SMs. (**c**) Ratio of the number of valid SMs to the number of waked SMs. (**d**) Ratio of the number of valid SMs to the number of invalid waked SMs. (**—**; \(\text{BDIM}_{\text{j}}\) -: distributed infectious disease model (DIDM)). Figure 10: The state of the CM at the 30 th time interval. The WC performance of the CMs is shown in Figure 12. The detailed calculation data are listed in Table 5.0 Figure 12b shows that the number of valid waked CMs is no different across the whole process for the two methods, while Figure 12a shows that the number of waked CMs via the BDIIM is clearly less than that achieved via the DIDM method. During the whole process, the maximum number of waked CMs via the BDIIM method is approximately 50 after 10 s, while the maximum number via the DIDM method reaches more than 150 much more rapidly. Naturally, the ratio of the number of valid waked CMs to the total number of waked CMs demonstrated by the BDIIM method is much higher than that proposed by the DIDM method, as shown in Figure 12c, which means that the efficiency of the waked CMs is improved greatly using the BDIIM method. The average efficiency after 10 s using the BDIIM method is estimated to be approximately 65%, compared with an average efficiency of just 21% achieved by the DIDM method. In addition, the number of idle sensor nodes is also given in Figure 12d, and it can be seen that the average number of idle nodes is 15 in the BDIIM method, which is much less than the 127 that would occur using the DIDM method. The percentage of the number of invalid waked CMs for the BDIIM method compared with the DIDM method is just 12.4%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Number of Waked** & \begin{tabular}{c} **Number of Valid** \\ **Waked CMs** \\ \end{tabular} & \
\begin{tabular}{c} **Ratio of Number of Valid** \\ **CMs to the Number of** \\ **Waked CMs (after 10 s)** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Invalid Waked** \\ **CMs (after 10 s)** \\ \end{tabular} \\ \hline DIDM method & 153 & 32 & 21\% & 121 \\ BDIIM method & 42 & 27 & 65\% & 15 \\ Improvement time & / & / & 3.1 & 12.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Data of the CMs performance of nodes in WC. Figure 12: The WC performance of CMs: (**a**) Number of waked CMs. (**b**) Number of valid waked SMs. (**c**) Ratio of the number of valid waked CMs to the number of waked CMs. (**d**) Number of invalid waked CMs. (—: BDIIM; –: DIDM).