# Research on Disease Spreading Behavior Oriented to Three-Layer Complex Networks
## 5 Immunization Strategy of Intermediary Layer  
In the three-layer complex networks, the intermediary layer connects the upper and lower layers, and the probability of the inter-layers link controls the average degree value of the network, which makes the network characteristics appear as multi-peak phenomenon, and the average degree value directly affects the disease-spreading behavior. Therefore, the intermediary layer plays an important role in the global spreading procedure. Through the intermediary layer's mediating role, the disease can spread across different types of networks, which greatly extends the range of spread and causes serious hazards for different groups. It is an important idea that we set the immunization strategies in multi-layer networks to suppress such cross-layer disease spreading from the intermediary layer. In reality, there are many ways to suppress the disease spread, and the most effective way is to isolate the infection source in time and avoid contact with the infected individuals. Based on such theory, the corresponding disease immunization strategy is formulated in conjunction with an analysis of the structural properties of the three-layer networks and the factors influencing the disease spread. For the three-layer network EEE, three-layer network EWE, and three-layer network EBE, the disease spread is firstly suppressed by reducing the probability of cross-layer links between the intermediary layer and the other layer. Secondly, the spread of disease can also be suppressed by reducing the link tightness in the intermediary layer, and it also can be suppressed by appropriately reducing the number of individuals in the intermediary layer. For the different networks, the corresponding immunization strategies are designed. The three kinds of immunization strategies are designed on the three-layer network EEE, in which each new one is changed based on the previous strategy parameters, and such design is more obvious to create an experimental comparison and is more useful for the results analysis. The initial network parameters are set as \(N_{\alpha}=500\), \(N_{\beta}=450\), \(N_{\gamma}=300\), \(P_{\alpha}=P_{\beta}=P_{\gamma}=0.1\), and \(P_{\alpha\beta}=P_{\beta\gamma}=0.2\). Strategy 1: reducing the link probability of the intermediary layer, and setting the inter-layer link probability to \(P_{\alpha\beta}=P_{\beta\gamma}=0.05\). Strategy 2: continuing to reduce the intra-layer link probability of the intermediary layer based on strategy 1, and \(P_{\beta}=0.01\). Strategy 3: reducing the number of nodes in the intermediary layer based on the above experiments, and \(N_{\beta}=350\). Figure 12(a) shows the experimental results of the three strategies, which show that all three strategies can effectively suppress the spread of the disease; meanwhile, it can reduce the spreading speed and the density of the infected individuals. On the three-layer network EWE, three immunization strategies are also formulated. Since the analysis in Section 4.2 above shows that the number \(k\) of neighboring nodes has little impact on the spread, such factor is not considered. On the three-layer network EWE, the immunization strategies are consistent with the network EEE. The experimental results are shown in Figure 12(b); the spreading speed of the network is significantly reduced after adopting strategy 1, and the spread is not significantly suppressed by reducing the  
Figure 12: Influence of diffusion rate on spreading in three-layer EBE network. intra-layer link probability and reducing the number of nodes in the intermediary layer. Therefore, it is the inter-layer link probability that affects the spreading procedure. The two immunization strategies are formulated on the three-layer network EBE, and the inter-layer link probability is first reduced and then the number of nodes in the intermediary layer are reduced. The experimental results are shown in Figure 13c.