Epidemic Spreading On Two-layered Networks

With the discovery of small world networks and scale-free networks,the study of graph theory has entered into the era of complex networks.Compared with reg-ular networks and random networks,the conclusions obtained from the research on complex networks are better fitted to real systems.The complex network method is applied in biology,sociology,economics and other fields,and has achieved amazing results.The epidemic is a devil,inexorably hangs on for thousands of years.Every time the epidemics outbreak,people are threatened,and caused great economic loss-es.The epidemic is a hot spot in scientific research,and the research on the epidemic of complex networks has made enormous achievements,providing theoretical support for the prediction and control of disease.At the beginning,the study of epidemic propagation is limited to static networks,and the edges between nodes and nodes are fixed.It is found that when the network size is very large,the spread of the epidemic in the scale-free network disappears.Epidemics can spread between animal and human networks,such as H1N1 in 2009.So the single-layer network has difficulty in describing such scenes.The researchers constructed a two-layer network model,where is found that the two-layer network model can better match the real system,therefore,the focus of our work is transferred to the two-layer network.It is found that the threshold of epidemic spreading on two-layer networks tends to be the same.The statistical results of Jeffries et al.in the United States show that bisexual individuals are the link between homosexual and heterosexual couples.Inspired by this,in the first work,we established a two-layer network model with the propagators.Our model with the two-layer network model in the past are essentially different,ma-terial exchange accomplished by the jumping of propagators between the two layers of the network,rather than by inter-layer connections.We found that the existence of propagator can also make the two-layer network's epidemic threshold tend to be the same,at the same time propagator also plays a role of pathogen transport.This work tells us that the propagator plays a key role in the spread of the epidemic in a two-layer network model.Our disease control should focus on propagators.This result can easily be expanded to the research of other issues.For example,there are two cities,where epidemics spread locally.Travelers(businessmen,tourists,drivers)will transport pathogens in the two cities.We introduce travelers to describe this scene.We have studied the effects of the number and behavior of travelers on the spread of epidemics on the double decks.We find that our model presents many new phenomena.It is very different from the traditional strong coupling or fixed connected two-layer network.Same as other two-layer network,we observe the joint thresh-old.However,this threshold is between the two independent thresholds of two layers.Travelers' distribution can not determine the threshold monotonously,thus we need to carefully design the strategy of distribution.From a practical perspective,i.e.,un-der the premise of ensuring material transportation,if we want to limit the outbreak in two cities,we can not unilaterally restrict the travel,but regulate the migration direc-tion.In the course of the study,we also find an interesting observation angle,which is helpful to check the spread of the network to the epidemic.