Research On Spreading Behaviors On Social Networks

The relationships between entities in human society can be described through complex networks,such as social contact network,scientists collaboration network,transportation network and the Internet.The research of complex networks not only studies the structure of the network itself,also focuses on the spreading dynamics on the network.Based on the difference between spreading behaviors on the network,the spreading dynamics on the network can be classified into three categories: the simple biology spreading,complex social contagion and the coupled spreading.The simple biology spreading mainly refers to the dynamics process of single contact,such as information,rumors,computer viruses and epidemics,etc.,which is enough to cause the infection.Complex social contagion mainly focus on the adoption of health behavior,innovation and other dynamical processes that require social reinforcement effects for the spread.The coupled spreading means the two dynamical processes interact spreading.The aim of studying different spreading behaviors is to apply theoretical research to the prediction and control processes of the real spreading.This thesis mainly includes the following three aspects:First,we study the impacts of the complex network structure on the simple biology spreading.As the epidemic infection occurs between the members of households,schools,workplaces and communities,this thesis studies the impact of human contact patterns on the predictability of the epidemic reproduction number.A realistic contact network model is built firstly based on highly detailed sociodemographic data from Italy.For a unknown epidemic occurring in future,we establish the spreading model and simulate an infection transmission process on these networks accounting for the natural history of influenza.By analyzing all individual-level transmission events and measuring the reproduction number,we find the reproduction number increases with time first and then decreases with time.This result is in contrast with the prediction of the classical theory where the reproduction number keeps unchanged in the initial spreading of the epidemic.To verify the robustness of our result,the data of the 2009 H1N1 virus in Italy is collected,and the spreading parameters of its propagation are estimated by using microscopic Markov chain.Finally,we simulate the spreading process of H1N1 virus and recording all individual-level transmission events.We find the classical theory fails to predict the epidemic reproduction number both in real data and the simulation results.To make up this deficiency,an algorithm is proposed based on the Bayesian theory which can accurately predict the effective reproduction number of epidemics.Considering the time-varying and multi-layered nature of human contact,an epidemic spreading model on time-varying multiplex network is proposed.It is found that increasing the proportion of interlayer coupling nodes or increasing the number of layers in the network will promote the spread of epidemics and reduce the epidemic outbreak threshold.When the average degrees of the two network layers have a large difference in the multiplex network,the spreading process on the network with a larger average degree drives the spreading of the entire system.These studies have deepened our understanding of the spread of real epidemics and provide new ideas for the prediction and control of epidemics.Then,we study the impact of individual’s behavioral responses on complex social contagion.From the local point of the network,where the effects of multiple individuals interacting on the network are far greater than the sum of the effects of these individuals when they are independent,we first propose a model to study the effects of neighbors’ synergies on the reversible spreading dynamics.The simulation results show that when the strength of the neighbors’ synergies is greater than a certain critical value,the fraction of infected nodes in the steady state increases explosively with the increase of the transmission probability.The established mean field theory is a good explanation of this explosive spreading phenomenon qualitatively.In addition,considering the state information of individual’s neighbors,the developed master equations accurately predict the simulation results.On the other hand,from the point of the global structure of the network,the impact of opinion leaders on individual’s behavioral adoption in social networks is studied.When opinion leaders are randomly chosen from the network,it is found that opinion leaders not only accelerate the adoption process of behavior,but also increase the range of network’s mean degree that the behavior can outbreak.When opinion leaders are chosen from the network with the largest degrees,it shows that there is an optimal mean degree of opinion leaders,which makes the behaviors outbreak on the network with the lowest mean degree.These findings provide new basis for the modeling of real data and the explanations for the observed spreading phenomena in the real world.Finally,we study the effect of coupling mechanism on coevolution spreading dynamics.In the asymmetric interacting spreading of information diffusion and disease spreading,the impacts of complex behavioral responses on the epidemic dynamics and the control effects are explored.It is found that this complex adoption behavior in the communication layer can significantly enhance the epidemic threshold and reduce the final infection rate.By defining the social cost as the total cost of vaccination and treatment,it can be seen that there exists an optimal social reinforcement effect and optimal information transmission rate allowing the minimal social cost in preventing the spreading of the disease.When the coupling process consists of two successively related complex contagions,the simulation and theory results find that the inhibition effect of the first behavior leads to the continuous phase transition of the second behavior becoming a discontinuous phase transition,and the synergistic effect will cause the discontinuous phase transition of the second behavior to become a continuous phase transition.In addition,we articulate a synergistic behavior spreading model on a double layer network,where the key manifestation of the synergistic interactions is that the adoption of one behavior by a node in one layer enhances its probability of adopting the behavior in the other layer.A general result is that synergistic interactions can greatly enhance the spreading of the behaviors in both layers.A remarkable phenomenon is that the interactions can alter the nature of the phase transition associated with behavior adoption or spreading dynamics.In particular,depending on the transmission rate of one behavior in a network layer,synergistic interactions can lead to a discontinuous(first-order)or a continuous(second-order)transition in the adoption scope of the other behavior with respect to its transmission rate.A surprising two-stage spreading process can arise: due to synergy,nodes having adopted one behavior in one layer adopt the other behavior in the other layer and then prompt the remaining nodes in this layer to quickly adopt the behavior.The results of these co-evolutionary transmissions not only provide a new method for optimal control of a single simple disease,but also have certain application value for how to promote complex contagion behaviors such as health and innovation.