## 3 The Corresponding Relationship between the Proposed BDIIM and Node Wake-Up Process  
In this section, similarities between sensing nodes in sensor networks and individuals in epidemic areas are established. * Collaboration between the self-organized sensor nodes is similar to the infectious interactions between these individuals. * A sensor node obtains the target information using the SM or CM while an individual is infected through DI or CI. * For the sensor nodes in WSNs, when a sensor node finds a target using its SM, this node then communicates with its neighbors via a CM. For the individuals in an epidemic area, when an individual is infected by DI, this individual then propagates the pathogen to their neighbors by CI. * Using a sensor node SM in a \"wake\" state, it is possible to find the target, while DI of an individual with immune deficiency may occur with the presence of the superspreader. * A sensor node CM in the sleeping state cannot obtain target information, while CI of an individual with immunity does not occur with their neighbors. Based on these similarities between the BDIIM and the sensor node wake-up process, parameter correspondence between BDIIM and sensor nodes are established, as listed in Table 1. Further, for the \(k\)th individual and corresponding \(k\)th sensor node, the corresponding activity relationships between them are listed in Table 2.  
Corresponding relationships composed of seven pairs of states between BDIIM and the sensor's WC state are shown in Figure 4. Each pair of states contains a state of the BDIIM and a WC state marked in a yellow and gray box, respectively. Each pair of states denotes the corresponding relationships between the BDIIM and the sensor's WC states. According to the above proposed algorithm in Section 2 and the settings in this section, when a target appears, all of these seven groups of states will transform continuously to achieve wake-up control of each sensor node. There are two modes for the sensors: on duty and off duty. When the sensor is in \"on duty\" mode, the processing unit is powered on, at least one of the SM and/or CM is powered on, and the sensor is capable of processing the sensory messages. On the contrary, when the sensor is in \"off duty\" mode, the processing unit (PU) is powered off, and the SM and CM are either turned off or turned on to wait for wakeup signals. The corresponding relationships between the WC states and sensors states are listed in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter of WC** & **Parameter of BDIIM Model** & **Symbol** \\ \hline Target & Epidemic superspreader & \\ \(k\)th sensor node & \(k\)th individual & \(I_{k}\) \\ Sensing range & DI radius & \(R_{s}\) \\ Communication range & CI radius & \(R_{c}\) \\ Probability that a waked node & Probability that an individual with immune & \\ detects the target within & deficiency to DI within the epidemic’s DI zone is & \(P_{d}\) \\ sensing range & infected by the superspreader & \\ Probability that a node falsely & Probability that an individual is infected by an & \\ confirms the existence of the target & unknown cause instead of the superspreader & \(P_{f}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter correspondence between the BDIIM and the sensor nodes.