Research On Heterogeneity Of Spreading Dynamics And Immunization Strategies Based On Social Network

With the increasing networking of human society and the rapid development of information technology,the spread of rumors,the adoption of healthy behaviors,and the adoption of innovations are widespread in real social networks.While these social contagion behaviors bring convenience to daily life,they also will adversely affect the social economy and human production and life.Compared with the independent infection probability of any two contacts in biological contagions,the spreading mechanism of social contagion phenomena such as information spreading and behavior adoption is more complicated.There is a reinforcement effect in social contagions.Social contagion is the expansion and application of biological contagions,and it is also the research foundation of social-biological contagions.Therefore,studying social contagion mechanisms and proposing strategies to control social contagions is an important research topic,which is of great significance for maintaining social stability and advancing research on network contagion dynamics.At present,the research on social contagions with the social reinforcement effect based on non-redundant information memory is receiving extensive attention from researchers.For the convenience of description,it is said that what is transmitted in social contagions is "behavior".Each individual can remember the behavior information passed to him by all neighbors.The probability of behavior adoption when the behavior information is received again depends on the number of previously received behavior information,and the more behavior information previously received,the greater the probability of adoption.That is,there is a reinforcement effect in social contagions.Considering the limited amount of information that an individual can provide,a non-redundant information transmission method that allows only one successful transmission of information between a pair of individuals is adopted.This article will be divided into two parts to study the dissemination heterogeneity and immune strategy of non-redundant information memory social contagions.The first part of this article studies the impact of the adoption threshold heterogeneity on the non-redundant information memory social contagions.The differences in personal characteristics often affect the willingness of individuals to adopt behaviors,leading to the heterogeneity of behavior adoption thresholds.First,a heterogeneous propagation threshold model is proposed,in which the adoption threshold obeys Gaussian distribution and is positively correlated with degree.In addition,an accurate edge-based compartmental theory is developed to perform dynamic analysis and outbreak threshold analysis on this model.Through a large number of experimental simulations and theoretical fittings on the ER network and the SF network,it can be found that increasing the mean of the adoption threshold distribution will inhibit social contagions,and how the standard deviation of the adoption threshold distribution affects social contagions depends on the size of the mean of the adoption threshold distribution.When the mean of the adoption threshold distribution is small,the outbreak threshold increases with the increase of the standard deviation of the adoption threshold distribution,and the system shows a continuous phase transition.When the mean of the adoption threshold distribution is large,the outbreak threshold decreases with the increase of the standard deviation of the adoption threshold distribution.In this case,the phase transition when the standard deviation is small is discontinuous,and the phase transition when the standard deviation is large is continuous.The second part of this article studies the impact of immune strategies on the non-redundant information memory social contagions.The immune nodes in the network do not participate in the propagation process,which is equivalent to removing immune nodes and their connected edges from the network,and social contagion only occurs on the remaining network.We describe the social contagion process under a degree-based immunization strategy based on a non-Markov SAR propagation threshold model,where the value of the immune index determines the type of immunization strategy.Through the theoretical analysis of edge-based compartmental theory,as well as the simulations and theoretical fittings on the SF network,it can be found that when other conditions are the same,the targeted immunization can produce the best suppression effect on social contagions;increasing the immune index or the immune ratio will reduce the final behavior adoption size and increase the outbreak threshold.When the immune ratio is small,increasing the heterogeneity of the network degree distribution will reduce the outbreak threshold.When the immune ratio is relatively large and the targeted immunization strategy is adopted,the outbreak threshold will increase with the increase of the heterogeneity of the degree distribution.