To bolster the reliability of conclusions derived from the artificial random network, we introduced two real networks. Table 1 presents the number of nodes, degree of 1-simplices, 2-simplices. Real networks exhibit strong heterogeneity, making the approximation with mean-field theory unsuitable. Instead, we employ the microscopic Markov-chain approach (MMCA) for approximation [24]. For any node i in the network, the probability of the node being infected by epidemic A or B at time t can be
