# Research on Disease Spreading Behavior Oriented to Three-Layer Complex Networks
## 4 Modeling and Analysis of Three-Layer SIS Disease Spread Model  
Multi-layer networks incorporate the interdependence and inter-constrained relationships between different types of network groups, and they are more coincident with real networks. There have been studies on disease spreading on multi-layer complex networks, but they are generally exemplified by two-layer networks, where the top and bottom layers are constructed as the same network, and there are certain specificities in this type of network model. In reality, many diseases are transmitted through intermediary layers, for example, HIV is from chimpanzees, H5N1 and H7N9 are from birds, dengue virus is from mosquitoes, SARS virus is from civets and the Black Death, and plagues are from rodents. None of these diseases originate from human societies, but it ultimately poses a great danger to human life. In order to better analyze the spread characteristics of diseases in multi-layer heterogeneous networks, this paper constructs a three-layer complex network model that conforms to the cross-layer spreading characteristics of realistic diseases, in which only the intermediary layer changes, the inter-layers are connected by random approach, the number of nodes in the three single layers is not unique, and two intra-layer link method are not same. Therefore, three different types of groups, such as animal society, mediated group, and human society, are modeled and analyzed based on the multi-layer network model to explore the trend of disease spread in the cross-layer networks. The three different types of groups adopt appropriate immunization strategies  
Figure 2: Degree distribution of three-layer EEE networks. (**a**) Degree distribution of three-layer EEE networks; (**b**) degree distribution of three-layer EWE networks; (**c**) degree distribution of three-layer EBE networks. using the properties of the intermediary layer to suppress the damage caused by such cross-layer disease spread. Therefore, exploring the influence of the intermediary layer on the overall spreading procedure is the central focus in this paper. Different parameters constructed by the three-layer network can lead to different spreading phenomena. In addition, the changes in the infection and recovery rates of the disease itself can also lead to changes of spreading procedure. Therefore, the analyses of the different effects of each parameter have an important implication for the spreading procedure and the adoption of the subsequent immunization strategies. The modeling procedure of the three-layer SIS disease spreading model proposed in this paper is shown in Figure 3 below. Firstly, this paper constructs three kinds of three-layer complex network models and analyzes the network degree distribution of three-layer EEE network, EWE network and EBE network, which constructs a detailed foundation for exploring the impact of network structure on spreading behavior. Secondly, the disease-spreading layer behavior in the three-layer complex networks under SIS disease-spreading mechanism is deeply studied. Based on the SIS-spreading mechanism, the spreading threshold in the three-layer network structure is analyzed. The theoretical derivation results are verified by simulation. It is concluded that the spreading threshold is closely related to the network average degree. At the same time, the influence of network structure characteristics on the spreading procedure and the influence of disease spreading rate on the spreading procedure are also deeply explored. Finally, the special properties of the intermediary layer of the three-layer network are analyzed, and the corresponding immunization strategy is formulated to effectively inhibit the spreading behavior. This paper is mainly based on the characteristics of the three-layer network structure to explore the cross-layer spreading behavior of diseases. Therefore, the innovation of  
Figure 3: Overview of the proposed solution.