| The study of analysis and control of spreading dynamics on complex network,such as spreading and immunity of epidemic diseases,spreading and control of computer virus and spreading and control of informations,have attracted wide attention of researchers in many fields because of its practical application value.With in-depth study of physical meaning and mathematical characteristics of network nature,it is found that many practical networks have common characteristic of community structure,such as social networks,Internet networks and online social networks.This dissertation is focused on studying the epidemic spreading behavior modeling and immunization on community structure networks.As assumption conditions of traditional epidemic spreading models are simpler,which is inadequate to describe the evolution process of epidemic spreading in real networks.So,in this dissertation,considering individuals' behavioral characteristics(e.g.,individuals' movement and individual behavioral responses),the spreading characteristics of virus(such as fatality rate and infection cycle)and the network structure feature(such as community structure and heterogeneous among communities),some novel epidemic spreading models are established to simulate and analyze the spreading process of epidemics in various real networks.And epidemic spreading dynamics and effective immunization strategies are studied on the basis of complex network theory.The main contributions of the dissertation are as follows:1.Modeling and analysis of epidemic spreading on homogeneous community networkBased on the classical homogeneous network model,a kind of homogeneous community structure network model with adjustable modularity coefficient is constructed,which can simulate some practical networks with different modularity coefficient.Considering the actual infection characteristics of different viruses,two kinds of epidemic models are established on this community network:(1)A novel SIS epidemic model considering the characteristic of community structure.A steady state analysis is conducted to solve the epidemic threshold and the final steady-state prevalence,and the theoretical results are verified by Monte-Carlo simulations.The theoretical and simulation results show that the epidemic threshold is inversely proportional to the modularity coefficient,and the epidemic prevalence is almost not affected by the changes of modular coefficients.(2)The SEIS epidemic model on the community structure network considering individuals' birth and death.In real life,many biological viruses have their infection characteristics,such as high fatality rate,longer infection cycle and so on.Thus,in the spreading process,there may be the birth of new individuals and the extinction of old individuals.Based on the community structure network,an epidemic spreading model considering individuals' birth and death characteristics is established,which can be used to simulate different kinds of viruses by changing the parameter of the epidemic model.A steady state analysis is conducted to study the effects of the birth rate and the death rate(including viral infection and other causes of death)on the epidemic spreading,and the epidemic threshold is solved either.The study results show that the epidemic threshold is inversely proportion to the birth rate and the modularity coefficient,and is proportional to the rate of death from any cause.2.Modeling and analysis of epidemic spreading on community network with heterogeneioty among communitiesIn real networks,when individuals are divided according to certain attributes,it can be found that there are heterogeneioty among communities.In view of this,in this dissertation,a community structure network model with adjustable heterogeneity among communities,and a mathematical epidemic model based on each community are presented.Then,the effects of heterogeneioty,modularity coefficient and location of infection sources on epidemic spreading process are studied,and epidemic threshold is deduced either.The study shows that:(1)In a community network with heterogeneioty among communities,the global epidemic threshold is between the maximum and minimum of the inner-communityp epidemic threshold;(2)When the average degree of the network is constant,the global epidemic threshold is inversely proportional to the heterogeneioty among communities;(3)Changing the location of the source of infection can only affect the spreading velocity,but it has little influence on the steady-state transmission prevalence.3.Modeling and analysis of epidemic spreading dynamics on dynamic community networkConsidering that contact patterns between individuals in real social networks can be divided into frequent contact and occasional contact,a dynamic small world network model with a modularized coefficient and a community structure is constructed,and a SIR virus propagation model on a dynamic small world community network with two types of long range jumping is established(the edge of the network is divided into fixed short range edge and time-varying random long range edge).The two models can be used to simulate the evolution process of virus propagation in real network,and the influence of individual movement on the evolution dynamics of virus propagation and its critical characteristics are analyzed.Through the analysis of differential dynamics equations,the threshold of virus propagation is obtained,and Monte Carlo simulation is used to verify the theoretical results.Theoretical analysis and simulations show that long range movement of the node not only affects the modular strength of the community,but also has great influence on the virus transmission process.The smaller the long range movement rate is,the greater the community strength and the smaller the critical value of the transmission are.In addition,the modularization coefficient is inversely proportional to the propagation threshold,that is,the greater the number of the community modularization system is,the smaller the critical value of the virus transmission is.4.An immunization strategy study considering the the influence of the nodes within and among communities on the static community structure networkThe characteristic of community strucure has an important influence on epidemic spreading and control,for example,some bridge nodes greatly promote the epidemic spreading between communities.While many immunization strategies neglect the influence of community structure characteristic.In view of this,this dissertation proposes a comprehensive immunization strategy accounting the community structure characteristic and individuals' influences(the impact of epidemic spreading within and among communities).The basic idea of the immunization strategy is to immune part of influential individuals within community and some bridge nodes to inhibit the epidemic spreading of inner-community and inter-community.On the basis of homogeneous and heterogeneous community structure networks,the proposed comprehensive immunization strategy is simulated and compared with the randomized immunization strategy based on the node centricity.The results show that the comprehensive immunization strategy proposed in this dissertation is more effective,and the inhibiting effect is better in the case of immune to the same number of individuals.5.An immunization strategy considering individual behavior in dynamic community networkThe topology of the actual network may change over time.And the individuals have autonomous behavior consciousness in the epidemic spreading process.Based on the SIR dynamic epidemic model,a hybrid immunization strategy considering individual avoidance awareness and immune behavior is proposed.By analyzing the spreading model that adopting the hybrid immunization strategy,the epidemic threshold is deduced and verified by Monte Carlo simulations.The results show that,the hybrid immune strategy can enhance the immune effect compared with the randomized immunization strategy based on the node centricity.And if we compare the control effects of self avoidance and immunization,the latter is superior to the former. |
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