The Heterogeneous Spreading And Immunization Strategy In Signed Networks

From human history,the epidemic of diseases has brought huge disasters to people’s lives.The modernization process has made the flow of people and materials more frequent,which has greatly accelerated the spreading of dis-eases.At the same time,in the presence of highly informatization,negative information such as rumors and negative public opinion is spread more widely and spread faster,bringing many negative effects on social stability and eco-nomic order.Therefore,it is of great significance to build a more real spreading model and design effective immunization strategies to suppress the spreading of diseases and rumors.Big data makes it possible to explore the deep social relationships between individuals.Social media generates a lot of emotional information(e.g.rating,evaluation,follow,black,etc.),which helps us to describe the deep relation-ships between individuals.The signed network is a powerful tool to describe emotional information.In real life,contact willingness between individuals is not homogeneous,it is affected by a variety of factors(e.g.relationships,in-terests,hobbies,etc.).Structural balance theory shows that individuals in the same balanced structure have a more friendly relationship,and it is easier to share information.Based on structural balance theory,we quantify contact will-ingness between individuals as heterogeneous contact probability.The more balanced structures formed by an edge,the larger contact willingness the indi-vidual connected by this edge.On this basis,we combine contact probability with spreading probability to make infection probability heterogeneous.In this way,the classic SIR model is extended to signed networks,and the heteroge-neous spreading model is defined in signed networks.Negative edges in signed networks represent negative relationships in so-cial life(e.g.enemy,distrust,hate,opposition,etc.).The emergence,increase,and gathering of negative relationships will lead to social tension and public panic,which undoubtedly have an impact on the spreading of diseases and in-formation.Based on the heterogeneous spreading model in signed networks,we study the impact of proportion and configuration of negative edges by numeri-cal simulation.The experimental results show that the balance of network and spreading coverage gradually decrease with the proportion of negative edges.It can explain social phenomena:with the increase of negative relationships,communal dissension increases,contact willingness decreases,and the spread-ing of diseases and information is suppressed.In addition,we also find that random configuration can suppress the spreading of diseases better than pref-erence configuration.By analyzing the performance of the spreading model in sparse networks and dense networks respectively,we find that the factors that affect the spreading in different density networks are different.In dense net-works,contact probability has a more significant impact on spreading;in sparse networks,the spreading path plays a more important role.The above conclu-sions can provide suggestions for epidemic prevention in different regions and environments.The immunization strategy in signed networks is also the focus of our studies.It is necessary to design an effective immunization strategy to sup-press some spreading behavior in signed networks,such as the spreading of rumors in online social networks and the spreading of diseases in social net-works.In the heterogeneous spreading model,we introduce sign information into the spreading dynamics by contact probability,which makes the infection probability among individuals heterogeneous,but does not change the structure of the network.Therefore,we apply the classical target immunization to signed networks by numerical simulation and analyze its performance in signed net-works from the two aspects,immunization efficiency and immunization cost.It is found that the degree centrality immunization has high efficiency and low cost,can effectively reduce the spreading path of diseases and information,and reduce contact willingness between individuals.This provides us with some ideas for epidemic prevention and the control of public opinion.