Epidemic Spreading On Multiplex Networks

As a social phenomenon closely related to public security,the spreading of epidemics has received intense research attention.Since single-layer networks can accurately describe the physical contact between individuals,they have been widely used to study epidemic spreading,and have achieved fruitful results.However,with the deepening of research,it is found that besides physical contacts,there are non-direct interactions between individuals,such as telephone,WeChat,etc.Though only direct contact could cause infection of an infectious disease,other types of contacts may strongly influence the spreading of epidemic,as people can take appropriate preventive measures after acquire the disease information.This leads to the coupling spreading process of mutual influences between epidemics and information.The framework of multiplex networks proposed in recent year can describe the coupling spreading process very well.Different from single-layer networks,multiplex networks have a set of nodes,but have more than one type of edges,so they can distinguish between different types of interactions in the system.This paper will use multiplex networks as a tool to study epidemic spreading.In this paper,based on multiplex networks,considering of the fact that an individual with more neighbors has higher possibility of getting infection,we propose a microscopic infection mechanism based on nodal degrees based on multiplex networks:after the individual learns the information that the disease is spreading,the preventive measures he takes are related to the number of his neighbors.Generally speaking,because individuals with more neighbors are more likely to be infected,they would take stronger preventive measures to lower the infection rate.To specifically describe the coupling spreading process between epidemics and information,we consider a duplex network.One layer is the physical contact layer,and the other layer is the communication layer.Epidemic spreading takes place on the physical contact layer,and we use the SIS model to describe it.The communication layer supports the spreading of information about the disease,and we use the UAU model to describe it Considering the diversity of individual behavior is the main innovation of this paper,we will focus on studying the influence of individual diversity on epidemic transmission in a duplex network.To quantitatively describe this infection mechanism,we introduce a suppression factor.We reveal the relationship between the epidemic threshold and the suppression factor by taking heterogeneous mean-field approach,and find that when the suppression factor begins to increase it has a prominent effect in suppressing the epidemic spreading,and this effect tends to be saturated when the factor is larger enough,which is consistent with the results of simulations.Second,we study the influence of interlayer degree correlation on the epidemic threshold,and find that the case of full correlation has a stronger suppressing effect on epidemic spreading.Finally,we find that the infection density varies with degree under different tendency for different values of suppression factor.When the suppression factor is small,the degree-based steady-state infection density increases with the number of neighbors.When the suppression factor is large enough,the degree-based steady-state infection density decreases as the number of neighbors increases.