# Research on Disease Spreading Behavior Oriented to Three-Layer Complex Networks
## 3 Construction of Three-Layer Complex Networks  
For the multi-path and multi-level problem of disease spread in real life, this paper proposes three special three-layer complex network models, such as three-layer EEE networks, three-layer EWE networks, and three-layer EBE networks. For the three-layer EEE network, the three single layers are respectively constructed by ER random links. For the three-layer EWE network, the first and third layers use ER random links, and the intermediary layer uses the WS small-world network modeling approach. For the three-layer EBE network, the first and third layers are also ER random networks modeling approach and the intermediary layer is a BA scale-free network modeling approach. In addition, all three networks use random links between layers, and the intra-layer and inter-layer link probabilities are all variables. Table 1 shows the definitions of the relevant parameters for the three-layer complex network model.  
The spreading mechanism in this paper applies the existing SIS disease-spreading mechanism; we apply this mechanism to the three-layer network constructed in this paper. Based on this model, we can better explore the spreading behavior of the three-layer network model. The three-layer network model in this paper focuses on the intermediary layer, and we also propose a construction algorithm of different three-layer network models, such as WEW, WEB, and BWE, which can greatly achieve the diversity of the three-layer networks. However, this paper only selects EEE, EWE, and EBE networks, and explores the related influences of spreading behavior in the three-layer network using different intermediary layers.  
At present, the current immunization strategy cannot effectively suppress the spread of disease in multi-layer networks. The traditional immunization strategies cannot effectively suppress the spreading procedure for more complex multi-layer networks. This paper takes advantage of the proposed models and sets different immunization strategies of the  
\begin{table}
\begin{tabular}{c l l l} \hline
**Parameters** & **Descriptions** & **Parameters** & **Descriptions** \\ \hline \(N_{\alpha},N_{\beta}\) & the number of nodes in layer \(\alpha\), \(\beta\) & \(P_{\beta},P_{\gamma}\) & the link probability in layer \(\beta\), \(\gamma\), \(\beta\), \(\gamma\in(0,1)\) \\ \(N_{\gamma}\) & the number of nodes in layer \(\gamma\) & \(P_{\alpha\beta}\) & the link probability between layer \(\alpha\) and layer \(\beta\), the value is defined from 0 to 1. \\ \(P_{\alpha}\) & the link probability in layer & & the link probability between layer \(\beta\) and layer \(\gamma\), the value is defined from 0 to 1. \\ \(m_{0}\) & the number of initial nodes in the BA network & \(m\) & the number of the added edges each time in the BA network \\ \(k\) & the number of neighboring nodes in the WS network & & \\ \hline \end{tabular}
\end{table}
Table 1: Three-layer complex network model parameters.  
intermediary layer, which effectively inhibits the spread based on the global networks and provides an experimental basis for inhibiting the across-layer disease spread in reality.