# Research on Disease Spreading Behavior Oriented to Three-Layer Complex Networks
###### Abstract  
Disease spreading in multi-layer complex networks often spreads among multiple populations with the help of media. In order to reveal the cross-layer spreading characteristics of diseases and control the cross-layer spreading of diseases by analyzing the inter-layer coupling mechanism in multi-layer complex networks, this paper proposes and establishes three kinds of three-layer disease spreading models based on SIS spreading mechanism, and analyzes the influence of spreading conditions, spreading speed, and diffusion range on disease spreading and corresponding immunization strategies. It is deduced theoretically that the spreading threshold of global network is relatively lower than that of a single-layer network. As the intermediary layer of the global network bridge, the strong coupling is more likely to cause the network to show multi-peak characteristic, and the influence of multi-peak transformation on the spreading speed is higher than that of the network generation mechanism. The immune strategy of isolating middle-layer nodes can effectively inhibit the spread of diseases. The research results of this paper are helpful to understand the spreading characteristics of various information in the real world. multilayer complex network; multi-peak characteristic; spread threshold; immunization strategy +
Footnote †: journal: Applied  
**Cited:**  
[PERSON] and [PERSON] et al. [9] found that having a strong community structure will inhibit spreading. In exploratory studies of disease spreading, the vast majority of attention is still focused on the phase transition of whether a disease can break out in a population. Based on the analysis of the phase transition, the spreading threshold of a disease is computed, which can be used to explore the nature of the spreading threshold, and to analyze the effect of changes of network structure and size on the spreading procedure. Studies of disease-spreading dynamics on complex networks aim to reveal the influence of network topology on disease-spreading behavior, or to analyze disease outbreak thresholds quantitatively or qualitatively based on infectious disease models, which can deepen the understanding of disease spreading behavior and predict disease outbreaks in populations. At the same time, the development of appropriate and effective immunization strategies is one of the key research topics in the dynamics of spreading on complex networks in order to suppress the negative effects of spreading. Based on taking into account the position of a node and connected edge properties in the networks, the main measure of immunization techniques is to protect the network by selecting key nodes in the network and then cutting off effective spreading paths. Most of the current researches on immunization strategies address the spreading of individual diseases based on a single layer network. The literature [10] compares the controlling effectiveness of random immunization and target immunization strategies on scale-free networks. Although target immunization is more effective in suppressing the disease, it requires traversing the global information of the network before taking action, and it is not applicable on the large-scale social networks. [PERSON] et al. [11] proposes a strategy of acquaintance immunization, which immunizes the neighboring individuals of being randomly selected individuals with a certain probability. In this strategy, individuals with a larger degree are more likely to be selected, resulting in a better immunization effect. The disease-spreading model refers to the basic mathematical model of disease spread, which mainly studies the spreading speed, space range, spreading path, dynamic mechanism, and other issues of diseases, so as to guide the effective prevention and control of diseases. Common infectious disease models are divided into SI, SIR, SIRS, and SEIR models. The existing models of disease spread are mainly studied based on single-layer networks, which do not conform to real-life situations and specific backgrounds.