A Study Of The Effects Of Heterogeneously And Adaptively Active Individual Behavior On Propagation Processes

Real-life transmission phenomena,such as the transmission of computer viruses,contagion diseases,and meme spreading,are influenced by individual human behavior at the microscopic level.Therefore,understanding the influence of individual behavior on the propagation process is the basis for predicting and controlling real propagation phenomena.Individual human behavior is characterized by heterogeneity and adaptiveness.The introduction and analysis of these two types of characteristics in the propagation process help understand the spreading process and potential risks.For clear studying the impact of the two aspects of individual behavior,this thesis discusses the effects of individual behavior on the spreading process into two cases based on whether the individual can recognize the state of propagation.When an individual is unable to identify the state of communication,the temporal pattern and structure of individual interactions play the core role.When an individual can recognize the state of communication,the process simultaneously affects and is affected by the individual's adaptive behavior.Since the temporally active pattern of human behavior depends on the data of the specific human behavior under consideration,this thesis first analyzes a specific data to derive a suitable depiction of the active pattern of human behavior corresponding to the data.This thesis then discusses the impact of the derived individual active patterns and individual adaptive behavior on the spreading process.This thesis will be divided into two main sections according to the research content.The first part of this paper analyzes the temporal patterns of individual communication events in empirical communication data and derives models that depict active patterns of human communication behavior.For individual communication event sequences,understanding how one event influences the next occurrence and whether the continuous events have long-range memory properties can help build appropriate models of human communication dynamics.In this paper,we investigate the statistical properties of two consecutive events using the evolution of the average residual time over the elapsed time of an individual event sequence and by obtaining the outburst fragments of the event sequence through threshold partitioning.We find that for individual communication event sequences,the occurrence of the latter event is influenced by the previous event for shorter elapsed times.In contrast,for longer elapsed times,the latter event occurs independently of the elapsed time.Further,this paper fits the empirical data through a segmentation model,where the parameters of the model are estimated from the division of the burst segments.In addition to the interval between event sequences,the presence or absence of long-range correlation properties also affects the understanding and modeling of human communication behavior.This paper uses traditional time series analysis methods and recently developed methods of mapping time series into complex networks to quantify the long-range correlation properties of individual event sequences.The analysis of the dataset considered in this thesis shows that the event sequences of a large number of individuals are not significantly different from the random disruption sequences.Therefore,the individual event sequences do not have significant long-range correlation properties.Based on the statistical analysis of communication event sequences,this thesis uses the hidden Markov chains approach to model individual communication dynamics.It then proposes mixed distributions to fit the empirical data.Through the parameters estimated from the empirical data,the mixed distribution can fit the original empirical data's interval distribution well.Most of the mixed distribution parameters are very close to each other in the population.Based on the assumption of independent homogeneous distributions for an event sequence's interval events,this paper derives the activity rate of an individual at any moment and the cumulative activity rate of an individual over time.The results show that the individual activity rate and the individual cumulative activity rate in a mixed distribution are quite different from those of an exponential distribution and a power-law distribution while keeping the same distribution expectations.The findings improve the understanding of human communication behavior's statistical properties on the one hand and provide a model of individual activity patterns in human communication behavior on the other.The second part of this paper investigates the influence of individual heterogeneity and adaptive behavior on spreading processes.The propagation process's evolution is mainly influenced by the individual active patterns when they are unable to recognize the state of propagation.This paper first ignores the influence of network structure.It assumes that active individuals are randomly paired with other active individuals to study how the speed of propagation,the propagation threshold,and the propagation range of the accompanying SIR propagation model change under different interevent time distributions.An extended SIR dynamic equation is given by introducing individual activity rates into the classical SIR equation,and the numerical solution of the extended SIR dynamic equation is consistent with the results of Monte Carlo stochastic simulations.By comparing the individual activity patterns derived from the data with the commonly assumed effects of individual activity on the propagation process,this paper shows the differences in the effects of different individual activity patterns on propagation,as well as the importance of appropriate individual activity patterns in understanding the accompanying propagation process.Further,this paper investigates the SIR propagation process driven by individual activity on both homogenous and scale-free networks.Numerical results show that on scale-free networks,small propagation thresholds correspond to small propagation ranges,but on homogeneous networks,the size of the propagation range varies across propagation parameters.The individual interval time distribution and the network structure have a complex influence on the accompanying propagation process.When an individual can recognize the state of transmission,the evolution of the transmission process is primarily influenced by the individual's adaptive behavior.As individuals identify their neighbors' state during the transmission process,they act to either inhibit or facilitate the transmission process,resulting in adaptive changes in the probability of individual infection with the transmission process.In this paper,we analyze the effects of adaptive allocation on neighbor contact intensity.At the same time,individuals maintain contact intensity and the effects of individual adaptive adjustment of contact intensity on the transmission process.The analysis shows that the individual's adaptive allocation to neighbor contact intensity effectively raises the transmission threshold,but the phase change of transmission becomes a first-order phase change.Individual contact intensity affects the probability of transmission,and thus the evolution of spreading processes.This paper analyzes how individuals adaptively increase or decrease the intensity of contact with other individuals according to their neighbors' propagation state.The results show that the individual-adapted contact intensity has the same propagation threshold as the classical propagation process.However,the individual-adapted increase in contact intensity leads to a first-order phase transition.In contrast,the individual-adapted decrease in contact intensity does not affect the kind of phase transition.The study results of human behavioral heterogeneity and the effects of adaptation on communication processes are useful for understanding and controlling real-life communication phenomena.