## 2 Establishment of a BDIIM for Node Wake-Up Control
### Modeling of the Biomimetic Infectious-Immune Process
#### 2.2.4 Six Sub-Processes of the Proposed BDIIM Algorithm  
Based on the above concepts and rules, six sub-processes as the core of the proposed algorithm of the BDIIM method are given: the occurrence probabilities of direct-infection and cross-infection, the immunity/immune-deficiency of direct-infection and cross-infection, the pathogen amount of direct-infection and cross-infection, immune memory, immune cell production, and pathogen accumulation under immunity state. The relationships between the six sub-processes of the BDIIM are shown in Figure 3. Further, the sub-processes can be divided into three groups: the infection mechanism, the immune mechanism, and the pathogen amount changing process. The infection mechanism determines whether DI and CI happens or not. The immune mechanism determines the amount of immune cells and whether the individual is immune to the disease or not. The infection mechanism and immune mechanism together control the changing process of the pathogen amounts. The accumulative pathogen amount, as the key parameter in BDIIM, determines the infection probability and the individual's immunity. Occurrence Probabilities of Direct-Infection and Cross-Infection  
When the individual is immune-deficient, they may be infected by the superspreader or other infected individuals. According to Rule 3, each individual infected by DI should be within the DI infectious distance. However, also according to Rule 3, the individuals outside the DI infection zone are also likely to be infected by other unknown factors. Therefore, the occurrence probability of DI (\(Dlp_{k}\)) of the \(k\)th individual is formulated as  
\[Dlp_{k}(t)= \begin{cases}P_{d}&if~{}~{}d_{k}(t)\leq R_{s}\\ P_{f}&if~{}~{}~{}d_{k}(t)>R_{s}\\ 0&otherwise\end{cases} ~{}~{}. \tag{1}\]  
According to Rule 2, more carried pathogen means a larger infection probability. Therefore, the probability of CI (\(Clp_{k}\)) of the \(k\)th individual is formulated as  
\[Clp_{k}(t)=f_{c}(~{}~{}V_{k}(t),~{}~{}~{}\Delta V_{k}(t-1)|V_{\min},~{}~{}~{}V_ {\max},~{}~{}~{}\mu~{}) \tag{2}\]  
where \(f_{c}(\cdot)\) denotes the general probability function. The probability function monotonously increases with the newly accumulated pathogen amount \(\Delta V_{k}(t)\) and the carried pathogen amount \(V_{k}(t)\). The initial value is set as \(\Delta V_{k}(0)=0\). The function parameters \(V_{min}\) and \(V_{max}\) denote the upper and lower bounds, respectively. The medical isolation parameter \(\mu\in[0,1]\) denotes the CI propagation degree. \(\mu=0\) means that susceptible individuals are absolutely isolated from the infected individual, and \(\mu=1\) represents that no isolation countermeasures are taken for susceptible individuals. **Remark 1**. : _The occurrence of probability is described as the immune deficiency probability in our previous work. Nevertheless, this description is not sufficient. It is common sense, and is also shown in Rule 10, that the susceptible individual should satisfy two conditions: the individual is immune-deficient, and this individual is within the infectious distance. However, as a matter of fact, not all susceptible individuals are infected after contacting infection sources. Therefore, the immune deficiency probability is confused with the infection probability. In this work, both are redefined: the probability that one individual is susceptible is formulated as the probability of immune deficiency, while the probability that one individual is infected after contacting the infection source is formulated as the infection occurrence probability._  
**Remark 2**. : _The probabilities described in Equation (2) are not unique; they only represent a general occurrence probability model about infectious disease. Users can design different occurrence probability functions for different kinds of disease via Equation (2)._  
**Remark 3**. : _The probability \(Dlp_{k}(t)\) depends on the superspreader's carried pathogen amount and the distance between the \(k\)th individual and the superspreader.