# Research on Disease Spreading Behavior Oriented to Three-Layer Complex Networks
## 4 Modeling and Analysis of Three-Layer SIS Disease Spread Model
In summary, we obtain that the spreading threshold of the single-layer network is greater than that of the global network in three-layer networks, and the spreading threshold of the network is related to the average degree value of the network; the larger the average degree value, the faster the spreading speed. To prove the theoretical derivation, experiments are carried out on the three-layer EEE network, three-layer EWE network, and three-layer EBE network, respectively. The results are shown in Figure 4, where the global network is the first to start spreading, followed by the single layer network, and the highest number of infections in the network is observed when the global spreading reaches a steady state. The spreading speed of the layer \(\alpha\) is greater than that of the layer \(\beta\), and the spreading speed of layer \(\beta\) is faster than that of layer \(\gamma\) in the three-layer EEE network; the main reason is that all three layers are ER random networks, and the layer \(\alpha\) of the network has the largest average degree, therefore, the faster the spreading speed, the smaller the spreading threshold. Figure 4: Spread threshold comparisons of the global and single layer of three-layer complex networks. In the three-layer EWE network, the spreading speed of the layer \(\beta\) is significantly lower than the other two layers of the network, the main reason is that the layer \(\beta\) is constructed using the WS small-world network method, and the network links are sparse and the average degree is smaller, so the spreading speed is the slowest. Similarly, In the EBE network, the layer \(\beta\) uses the BA scale-free network construction method, and the network degree distribution is extremely uneven; coupling with taking a smaller parameter value, consequently, the network is more sparse and the spreading speed is much slower. In the EEE network, the spreading speed of the layer \(\alpha\) is greater than that of the layer \(\beta\), and the spreading speed of the layer \(\beta\) is greater than that of the layer \(\gamma\); the main reason is that the three-layer network uses the ER random network, the average degree of the network is the largest, and thus, the spreading speed is much faster and the spreading threshold is also much smaller. Figure 5 demonstrates that the overall spreading threshold of the network is in good agreement with the theoretical derivation. This shows that the spreading threshold is closely related to the average degree in a uniform network. The parameter settings in Figure 4 are shown as follows:  
For the three-layer network EEE, \(N_{\alpha}=500\), \(N_{\beta}=400\), \(N_{\gamma}=300\), \(P_{\alpha}=P_{\beta}=P_{\gamma}=0.05\), \(P_{\alpha\beta}=P_{\beta\gamma}=0.1\). For the three-layer network EWE, \(N_{\alpha}=500\), \(N_{\beta}=400\), \(N_{\gamma}=300\), \(P_{\alpha}=P_{\beta}=P_{\gamma}=0.05\), \(P_{\alpha\beta}=P_{\beta\gamma}=0.1\), \(k=6\). For three-layer network EBE, \(N_{\alpha}=500\), \(N_{\beta}=400\), \(N_{\gamma}=300\), \(P_{\alpha}=P_{\gamma}=0.05\), \(P_{\alpha\beta}=P_{\beta\gamma}=0.1\), \(m_{0}=5\), \(m=5\).