# Information Propagation and Bionic Evolution Control of the _Sebar_ Model in a Swarm System
## 2 _Sebar_ Model of Information Propagation  
At present, there are many studies that have applied epidemic models to address information propagation. Based on previous research, this paper proposes the \(SEBAR\) information propagation dynamics model combined with swarm networks [19; 20]. To build the \(SEBAR\) model, five individual states within the swarm system are defined as follows: Susceptible (\(S\))--individuals that have not received the information; Exposed (\(E\))--individuals that have received the information and have potential propagation ability; Backed (\(B\))--individuals that support the current information and are actively spreading it; Against (\(A\))--individuals that oppose the received information and are actively spreading their opposition; Recovered (\(R\))--individuals that no longer receive or lose interest in the information. The transition relationships between these individual states are illustrated in Figure 1.  
The individual states' transition processes are explained as follows:  
1. When an individual in state \(S\) touches another individual in state \(A\), it will transfer to state \(E\) with probability \(p_{1}\). Then, the \(E\) individual changes to state \(A\) with probability \(p_{4}\). As a non-terminal state, the individual in state \(A\) will be in state \(R\) with the probability \(p_{6}\) to prohibit the information from spreading. Due to the forgetting mechanism, the individual in state \(R\) gradually loses interest in receiving information and returns to state \(S\) with probability \(p_{7}\). 2. After contacting an individual in state \(B\), the individual in state \(S\) transfers to state \(E\) with probability \(p_{3}\), and then it can change to state \(B\) with probability \(p_{5}\). Similarly, due to the inhibition mechanism, the individual in state \(B\) will transition to state \(R\) with probability \(p_{8}\). When the individual in state \(R\) loses interest in the received information, it will return to state \(S\) with probability \(p_{7}\). 3. When an individual in state \(S\) exchanges information with other individuals in state \(E\), it will change to state \(E\) with probability \(p_{2}\). After digesting and absorbing the information, the individual in state \(E\) transitions to state \(A\) with probability \(p_{4}\) or to state \(B\) with probability \(p_{5}\). Under the effects of the inhibition and forgetting mechanisms, the individual in state \(A\) or \(B\) will return to state \(R\), and the individual in state \(R\) will then be in state \(S\), respectively. When modeling information propagation using the mean-field theory, three assumptions for a homogeneous network are given [21; 22]:  
1. Each individual has the same probability of connecting to any other individuals, and its degree is approximately equal to \(\langle k\rangle\). 2. The state of each individual is independent of the states of its neighbors. 3. The number of individuals remains constant during the information propagation. Assume that the total number of the swarm system is \(N\), and the average degree is \(\langle k\rangle\). At time \(t\), the proportions of individuals in different states are \(S(t)\), \(E(t)\), \(B(t)\), \(A(t)\), and \(R(t)\) and satisfy \(S(t)+E(t)+B(t)+A(t)+R(t)=1\). When \(t=0\), the proportions of each state are \(S(0)=1\), \(E(0)=0\), \(B(0)=0\), \(A(0)=0\), and \(R(0)=0\). In addition, during the information propagation, the number of swarms in each state are greater than or equal to zero, and the number of individuals in different states equals the number of nodes in the swarm network [23; 24]. The differential dynamic equations of the \(SEBAR\) model, based on mean-field theory, are as follows:  
\[\left\{