## 2 Establishment of a BDIIM for Node Wake-Up Control
### Modeling of the Biomimetic Infectious-Immune Process
#### 2.2.3 The Proposed Biomimetic Distributed Infection-Immunity Model  
Based on the concepts mentioned above in Section 2.2.1, the immune mechanism is given through five rules as follows:* (minimum immune cell amount) Each individual can produce more or less the same number of immune cells; in other words, there exists a normal level of immune cells when the organism is in a healthy state. * (monotonic property of immunity) Each individual agent has the immune ability to produce immune cells. The immune cells are modeled as macrophages, which can devour the pathogens. Therefore, the more immune cells that are produced, the more pathogens that will be killed. * (immune memory) The newly cured individual has an immune memory. Over a period of time, they are unlikely to be infected again. By the end of the memory period, the immune cell number will be decreased to the initial level. * (criterion of immunity deficiency) When determining whether an individual has immune deficiency, the following two conditions must be met: First, the individual is located within the infection distance. Second, the time that the individual is infected is outside of the time of immune memory. * (monotonic property of immune cell rising tendency) The production of immune cells is determined by the amount of newly accumulated pathogen. In other words, the higher the amount of newly accumulated pathogen, the more the organism suffers from the attack of the pathogen. At the same time, more immune cells in the body of the organism will be produced. Furthermore, when the newly accumulated pathogen amount becomes lower, implying that the organism is in a recovery state, more immune cells will be produced, which leads to a rapid decline in the amount of pathogens in the organism. Based on Rules 7-11, the immune response against the invading pathogen is established. The functional flow process of the proposed BDIIM method is given first, as shown in Figure 2. It can be seen that a superspreader, as a source of infection, could infect N individuals simultaneously by direct infection (DI). These individuals experience cross-infection (CI) with each other. For each individual inside this model, there are four functional processes: pathogen accumulation, DI immunity/immune deficiency, immune cell production, and CI immunity/immune deficiency. Based on these concepts and the rules showed above, the proposed algorithm of the BDIIM, composed of six sub-processes, is further established and clarified in the next section. Figure 2: Functional flow process of the proposed biomimetic distributed infection-immunity model (BDIIM) method. Some notations for the BDIIM method are also given as follows. * The individual sets are denoted by \(I=\{I_{1},...,I_{k},...,I_{n}\}\). The subscript \(k\) represents the corresponding variable related to the \(k\)th individual. The distance between individual \(I_{i}\) and \(I_{j}\) is denoted by \(D(I_{i},I_{j})\). Denote the distance between the \(k\)th individual and the superspreader in the \(t\)th time interval by \(d_{k}(t)\). Denote the neighbor collection (including itself) of the \(k\)th individual by \(N_{k}=\{I_{j}\mid D(I_{j},I_{k})\leq R_{c},j=k\}\), and \(R_{c}\) is the CI radius. * A Boolean identification variable \(RDp_{k}(t)\) denotes immunity and immune deficiency to DI of the \(k\)th individual in the \(t\)th time interval by \(RDp_{k}(t)=0\) and \(RDp_{k}(t)=1\), respectively. The immunity and immune deficiency to CI of the \(k\)th individual in the \(t\)th time interval is denoted by \(RCp_{k}(t)=0\) and \(RCp_{k}(t)=1\), respectively. * The occurrence probability of DI and CI of the \(k\)th individual in the \(t\)th time interval are denoted by \(Dlp_{k}(t)\) and \(CIp_{k}(t)\), respectively. \(Dlp_{k}(t)=1\) happens with probability \(P_{d}\) when the individual is within the epidemic's DI zone, or with probability \(P_{f}\) when the individual is infected by unknown causes instead of the considered pathogen.