# Research on Disease Spreading Behavior Oriented to Three-Layer Complex Networks
###### Abstract
This paper mainly uses a multi-layer complex network to simulate the relationships between objects in real life, which further accords with the actual situation. Therefore, it is of great significance to study disease-spreading models on multi-layer complex networks. With the complexity of network models and the diversification of disease spreading, the study of spreading models on multi-layer complex networks [12] and immunization strategies has attracted extensive attention from many scholars. For complex and large social systems, traditional single-layer networks can no longer fully and effectively reveal the nature of real systems, and may lead to misrepresentation of real-world phenomena. Therefore, multi-layer networks have emerged. Multi-layer networks use different types of connected edges belonging to different levels of the system to describe the interactions of system entities in different link relationships, so as to effectively demonstrate the heterogeneity of nodes and the diversity of being connected edges, and it has become a hot topic in the field of network science. [PERSON] et al. [13] proposed and constructed four three-level super-network models based on a mixture of small-world and scale-free network models, and defined a two-level cross-degree to represent the competing and cooperative relationships between nodes at different levels. In the literature [14], two-layer ER and two-layer BA networks were constructed, and the influence of the association degree was researched for nodes between different layers. In the study of disease spreading in multi-layer networks, [PERSON] et al. [15] analyzed the spreading dynamics of interacting diseases from two perspectives: spreading threshold and disease outbreak, and further investigating the impact of interactions between diseases on immunization strategies. [PERSON] et al. [16] explored the epidemic spreading process on two-layer interaction networks and proposed three different models to describe the cooperative diffusion procedure on interconnected networks. [PERSON] et al. [17] summarized the spreading dynamics on multi-layer networks separately. The SIS spreading mechanism is the most basic and common in real life, and it is suitable for describing diseases such as influenza, which can recur after being cured. The three-layer network model is also a good description of the spreading characteristics of cross-layer diseases. Therefore, this paper adopts a three-layer complex network disease spreading model based on the SIS mechanism that generally conforms to the structure of real-life network systems and the characteristics of diseases. The novelty of the three-layer complex network construction algorithm is that the number of nodes within each individual layer is variable, and two single layers among three layers use the different construction algorithms. Due to using different construction algorithms, each single-layer network has a different average degree, resulting in a multi-peaked distribution for the overall degree of the network. The multi-peaked feature makes the network model more complex, while the different number of nodes in each layer makes it more relevant to the actual networks. The topological properties of the multi-layer networks and the influencing factors of disease spread are combined to investigate the dynamic behaviors of the disease spread. At the same time, the multi-peaked feature of the network provides a theoretical basis for the formulation of disease immunization strategies. In the spreading field in the real world, whether it is the virus spread of the computer, the rumor spread in information communication, or the disease spread crossing species, they have different spreading characteristics, and the basis of spreading lies in the interaction of different network types. The research of this paper is used to explore the cross-layer spreading behavior.