# 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  
First, the influences of different types of networks on spread behaviour is explored based on the different peak characteristics of the three-layers complex networks. As shown in Section 3.4, it can generate multi-peak phenomenon for the networks due to the difference of the average degrees of the single layer networks, and the effect of the average degree of the network on the spreading situation is then explored. For the three-layer EEE network, \(N_{\alpha}=450\), \(N_{\beta}=400\), \(N_{\gamma}=350\), \(P_{\alpha}=P_{\beta}=P_{\gamma}=0.1\), and \(P_{\alpha\beta}=P_{\beta\gamma}=0.1\). For the three-layer EWE network, \(P_{\alpha}=P_{\gamma}=0.12\), \(P_{\beta}=0.5\), and \(P_{\alpha\beta}=P_{\beta\gamma}=0.12\). For the three-layer EBE network, \(P_{\alpha}=P_{\gamma}=0.11\), \(m_{0}=20\), \(m=10\), and \(P_{\alpha\beta}=P_{\beta\gamma}=0.11\). With the above parameter settings, the overall average degree of all three networks is \(69\). The spreading threshold and spreading speed of the three different types of three-layer complex networks are the same as shown in Figure 6. It has been verified through many experiments that the spreading procedure of the whole network is consistent under the condition of the same average degree of the network, which does not matter with regards to the structure type or parameter changes of the network, therefore, the average degree of the whole network is the main factor affecting the whole spreading procedure, in other words, the larger the average degree, the wider the spreading range and the faster the spreading speed. The different peak properties are determined by the differences in the average degree of the single layers of the network, so there is no obvious regulation between the average  
Figure 5: Global spreading thresholds and its simulation fitting. degree and the peak of the network. Therefore, the factor affecting the network-spreading behaviour is the size of the average degree of the network in a uniform network; it is not relevant with the network type. Second, the effect of the construction parameters of the network on the spreading procedure is explored for the different three-layer complex network construction algorithms. For comparison, the network size is unchanged, they are \(N_{a}=500\), \(N_{\beta}=400\), \(N_{\gamma}=300\), and the infection rate and recovery rate are permanent. In the three-layer EEE network, two sets of experiments are set up to investigate the effect of the changes of the intra-layer connectivity probability on the spreading procedure. 1. When the probability of the intra-layer link in the three-layer EEE network gradually increases and the probability of the inter-layer link remains unchanged, the other parameters are set as follows: \(P_{a\beta}=0.1\) and \(P_{\beta\gamma}=0.1\). When the probabilities of the intra-layer links are 0.05, 0.1, 0.3, 0.4, and 0.5 for \(P_{a}=P_{\beta}=P_{\gamma}\), the spreading procedure is shown in Figure 7a; with the increase of the intra-layer link probability, the spreading speed is gradually accelerated and the density of the infected people gradually increases. When the probability of the intra-layer link increases to 0.3, the overall spreading speed of the network reaches the maximum value and the density of the infected nodes also reaches the maximum state. 2. The probability of the inter-layer link of the three-layer EEE network increases gradually, and the probability of the intra-layer link remains unchanged. We set the probability of the intra-layer link of the network as \(P_{a}=P_{a}=P_{a}=0.05\), and the probability of the inter-layer link is \(P_{a\beta}=P_{\beta\gamma}=\{0.05,0.1,0.2,0.3,0.5\}\), respectively. The network spreading is shown in Figure 7b. With the probability increase of the inter-layer link of the network, the spreading speed is gradually accelerated, and the number of infected nodes is also increased.