# Research on Disease Spreading Behavior Oriented to Three-Layer Complex Networks
## 4 Modeling and Analysis of Three-Layer SIS Disease Spread Model
### Influence Analysis of the Three-Layer Network Structure on Spread
When the inter-layer link probability increases to 0.3, the number of infected nodes in the network reaches the maximum value, but the spreading speed deviates slightly. Figure 6: The spreading trends of three kinds of three-layer complex network under the same average degree. Figure 7: Influence analysis of the three-layer complex network EEE’s parameters on spreading procedure, (**a**) shows the influence of the intra-layer link probability, (**b**) shows the influence of the inter-layer link probability. In the three-layer EWE network, we investigate the effect of the intra-layer and inter-layer connectivity probability on spreading procedure, the k values of the number of neighboring nodes in the network are also experimentally compared. Three sets of experiments are set up to investigate the effect of the changes of the network parameters, which are slightly accelerated, but the node density is the same when reaching the steady state, and there is no significant change. With the increase of \(m_{0}\), the network-spreading speed does not accelerate the significant spreading procedure. 1. When the probability of intra-layer link gradually increases and the probability of the inter-layer link remains unchanged, the other parameters are set as follow: \(P_{\alpha\beta}=0.1\), \(P_{\beta\gamma}=0.1\), \(k=4\). When the probability of the intra-layer re-link is \(P_{\alpha}=P_{\beta}=P_{\gamma}=\{0.05,0.1,0.3,0.4,0.5\}\), the spreading procedure of the network is shown in Figure 8a. With the increase of the probability of the intra-layer link, the spreading speed is gradually accelerated, and the density of the infected people in the network is also gradually increased. When the intra-layer link probability increases to 0.3, the overall propagation speed of the network reaches the maximum value, the density of the infected nodes is also in the maximum state. 2. When the number of the neighboring nodes \(k\) increases, the spreading procedure is shown in Figure 8b, and the results show that the value of \(k\) does not have an effect on the spread. 3. When the probability of the inter-layer link increases, i.e, \(P_{\alpha\beta}=P_{\beta\gamma}=\{0.05,0.1,0.2,0.3,0.5\}\), the network-spreading procedure is shown in Figure 8c. As the probability increases of the inter-layer link, the spreading speed is gradually accelerated and the number of infected nodes is increased. When the probability of the inter-layer link increases to 0.3, the number of infected nodes in the network reaches the maximum value. In the three-layer EBE network, two sets of experiments are conducted to investigate the effect of the inter-layer link probability and the parameters \(m_{0}\) and \(m\) on the spreading situation in the BA scale-free network. 1. To investigate the effect of the parameters \(m_{0}\) and \(m\) on the spreading procedure, the parameters \(m_{0}\) and \(m\) are set to \(m_{0}=\{20,10\}\) and \(m=\{10,5\}\), and the spreading result is shown in Figure 9a. As the value \(m\) increase, the whole spreads smoothly, and there is no change in density at steady state. 2. When the probability of the inter-layer link of the network increases, the experimental results are shown in Figure 9b for \(P_{\alpha\beta}=P_{\beta\gamma}=\{0.05,0.1,0.2,0.3,0.4\}\). With the increase of the probability of the inter-layer link, the spreading speed is accelerated, and the spreading speed reaches the maximum value when the probability of the inter-layer link reaches 0.3, and the density is also maximum at steady state. Figure 8: Influence analysis of the three-layer complex network EWE’s parameters on spreading procedure, (**a**) shows the influence of the intra-layer link probability, (**b**) shows the influence of \(K\) value, (**c**) shows the Influence of inter-layer link probability.