Modular Epidemic Spreading in Small-World Networks

We study the epidemic spreading of the susceptible-infected-susceptible model on small-world networks with modular structure. It is found that the epidemic threshold increases linearly with the modular strength. Furthermore, the modular structure may influence the infected density in the steady state and the spreading velocity at the beginning of propagation. Practically, the propagation can be hindered by strengthening the modular structure in the view of network topology. In addition, to reduce the probability of reconnection between modules may also help to control the propagation.     

Periodic Wave of Epidemic Spreading in Community Networks

It was reported by Cummings ef al. [Nature 427 （2004） 344] that there are periodic waves in the spatiotemporal data of epidemics. For understanding the mechanism, we study the epidemic spreading on community networks by both the SIS model and the SIRS model. We find that with the increase of infection rate, the number of total infected nodes may be stabilized at a fixed point, oscillatory waves, and periodic cycles. Moreover, the epidemic spreading in the SIS model can be explained by an analytic map.     

An Efficient Control Strategy of Epidemic Spreading on Scale-Free Networks

We present a novel and effective method for controlling epidemic spreading on complex networks, especially on scale-free networks. The proposed strategy is performed by deleting edges according to their significances （the significance of an edge is defined as the product of the degrees of two nodes of this edge）. In contrast to other methods, e.g., random immunization, proportional immunization, targeted immunization, acquaintance immunization and so on, which mainly focus on how to delete nodes to realize the control of epidemic spreading on complex networks, our method is more effective in realizing the control of epidemic spreading on complex networks, moreover, such a method can better retain the integrity of complex networks.     

Phase Transitions of an Epidemic Spreading Model in Small-World Networks

We propose a modified susceptible-infected-refractory-susceptible (SIRS) model to investigate the global oscillations of the epidemic spreading inWatts-Strogatz (WS) small-world networks. It is found that when an individual immunity does not change or decays slowly in an immune period, the system can exhibit complex transition from an infecting stationary state to a large amplitude sustained oscillation or an absorbing state with no infection. When the immunity decays rapidly in the immune period, the transition to the global oscillation disappears and there is no oscillation. Furthermore, based on thespatio-temporal evolution patterns and the phase diagram, it is disclosed that a long immunity period takes an important role in the emergence of the global oscillation in small-world networks.     

Eigenvector Localization in Real Networks and Its Implications for Epidemic Spreading

The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization properties of the principal eigenvector in real networks. We show that in most cases it is either localized on the star defined by the node with largest degree (hub) and its nearest neighbors, or on the densely connected subgraph defined by the maximum K-core in a K-core decomposition. The localization of the principal eigenvector is often strongly correlated with the value of the largest eigenvalue, which is given by the local eigenvalue of the corresponding localization subgraph, but different scenarios sometimes occur. We additionally show that simple targeted immunization strategies for epidemic spreading are extremely sensitive to the actual localization set.

     

Epidemic Diffusion on Complex Networks

Both diffusion and epidemic are well studied in the stochastic systems and complex networks, respectively. Here we combine these two fields and study epidemic diffusion in complex networks. Instead of studying the threshold of infection, which was focused on in previous works, we focus on the diffusion behayiour. We find that the epidemic diffusion in a complex network is an anomalous superdiffusion with varying diffusion exponent and that γ is influenced seriously by the network structure, such as the clustering coefficient and the degree distribution. Numerical simulations have confirmed the theoretical predictions.     

Spatiotemporal Characteristic of Epidemic Spreading in Mobile Individuals

We numerical simulate the propagation behaviour and people distribution trait of epidemic spreading in mobile individuals by using cellular automaton method. The simulation results show that there exists a critical value of infected rate fluctuating amplitude, above which the epidemic can spread in whole population. Moreover, with the value of infected rate fluctuating amplitude increasing, the spatial distribution of infected population exhibits the spontaneous formation of irregular spiral waves and convergence phenomena, at the same time, the density of different populations will oscillate automatically with time. What is more, the traits of dynamic grow clearly and stably when the time and the value of infected rate fluctuating amplitude increasing. It is also found that the maximal proportion of infected individuals is independent of the value of fluctuating amplitude rate, but increases linearly with the population density.     

Opinion Spreading with Mobility on Scale-Free Networks

A continuum opinion dynamic model is presented based on two rules. The first one considers the mobilities of the individuals, the second one supposes that the individuals update their opinions independently. The results of the model indicate that the bounded confidence εc, separating consensus and incoherent states, of a scale-free network is much smaller than the one of a lattice. If the system can reach the consensus state, the sum of all individuals＇ opinion change Oc（t） quickly decreases in an exponential form, while if it reaches the incoherent state finally, Oc（t） decreases slowly and has the punctuated equilibrium characteristic.     

Different Epidemic Models on Complex Networks

Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can besorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals' relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemicmodels on complex networks, and obtain the epidemic threshold for each case. Finally, we present numerical simulations for each case to verify our results.     

Different Epidemic Models on Complex Networks

Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals＇ relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each ease. Finally, we present numerical simulations for each case to verify our results.     

Criticality of Epidemic Spreading in Mobile Individuals Mediated by Environment

We investigate the critical behaviour of an epidemical model in a diffusive population mediated by a static vector environment on a 2D network. It is found that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behaviour near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.     

A Two-Stage Contact Process on Scale-Free Networks

We study a two-stage contact process on scale-free networks as a model for the spread of epidemics. We show that any virus starting from a single vertex with arbitrarily small infection rates can last for a super-polynomial time with positive probability if the power law exponent α>2. This is in sharp contrast with the mean-field analysis. The estimation of the metastable density is also provided.     

Effects of City-Size Heterogeneity on Epidemic Spreading in a Metapopulation: A Reaction-Diffusion Approach

We review and introduce a generalized reaction-diffusion approach to epidemic spreading in a metapopulation modeled as a complex network. The metapopulation consists of susceptible and infected individuals that are grouped in subpopulations symbolizing cities and villages that are coupled by human travel in a transportation network. By analytic methods and numerical simulations we calculate the fraction of infected people in the metapopulation in the long time limit, as well as the relevant parameters characterizing the epidemic threshold that separates an epidemic from a non-epidemic phase. Within this model, we investigate the effect of a heterogeneous network topology and a heterogeneous subpopulation size distribution. Such a system is suited for epidemic modeling where small villages and big cities exist simultaneously in the metapopulation. We find that the heterogeneous conditions cause the epidemic threshold to be a non-trivial function of the reaction rates (local parameters), the network’s topology (global parameters) and the cross-over population size that separates “village dynamics” from “city dynamics”.     

Epidemic Dynamics with Feedback Mechanism in Exponential Networks

We introduce a feedback mechanism to study the spreading of an epidemic by analytical methods and large scale simulations in exponential networks. It is found that introducing the feedback mechanism can reduce the density of infected individuals, Furthermore, it does not change the epidemic threshold （critical point） λc. These results can help us to understand epidemic spreading phenomena on social networks more practically and design appropriate strategies to control social infections.     

Epidemic Spread in Networks Induced by Deactivation Mechanism

We have studied the topology and epidemic spreading behaviors on the networks in which deactivation mechanism and long-rang connection are coexisted. By means of numerical simulation, we find that the clustering coefficient C and the Pearson correlation coefficient r decrease with increasing long-range connection μ and the topological state of the network changes into that of BA model at the end （when μ = 1）. For the Susceptible-Infect-Susceptible model of epidemics, the epidemic threshold can reach maximum value at μ = 0.4 and presents two different variable states around μ= 0.4.     

Rumor Spreading Model with Trust Mechanism in Complex Social Networks

In this paper, to study rumor spreading, we propose a novel susceptible-infected-removed (SIR) model by introducing the trust mechanism. We derive mean-field equations that describe the dynamics of the SIR model on homogeneous networks and inhomogeneous networks. Then a steady-state analysis is conducted to investigate the critical threshold and the final size of the rumor spreading. We show that the introduction of trust mechanism reduces the final rumor size and the velocity of rumor spreading, but increases the critical thresholds on both networks. Moreover, the trust mechanism not only greatly reduces the maximum rumor influence, but also postpones the rumor terminal time, which provides us with more time to take measures to control the rumor spreading. The theoretical results are confirmed by sufficient numerical simulations.     

基于样本块匹配的干涉图延拓方法

在快速傅里叶变换(FFT)方法处理单幅干涉图原理的基础上,提出一种基于样本块匹配的干涉图延拓方法,利用干涉图像的可信度和等照度线特征,来确定待填充块的优先权,然后在干涉图的已知区域寻找与待填充块最相似的样本块来进行填充。充分利用了干涉图的条纹特征,结合梯度变化方向有效地合成纹理信息,具有很好的延拓效果。最后将该干涉图延拓方法与傅里叶变换,合适的滤波函数和相位解包方法结合起来形成整套单幅干涉图处理方法。采用该单幅干涉图处理方法获得的波面峰谷值与Zygo移相干涉仪得到的平均相差不到λ/100,并且两种方法获得的波面均方根值平均相差不到λ/200。     

Reliability and Efficiency of Generalized Rumor Spreading Model on Complex Social Networks

We introduce the generalized rumor spreading model and investigate some properties of this model on different complex social networks. Despite pervious rumor models that both the spreader-spreader (SS) and the spreader-stifler (SR) interactions have the same rate α, we define α(1) and α(2) for SS and SR interactions, respectively. The effect of variation of α(1) and α(2) on the final density of stiflers is investigated. Furthermore, the influence of the topological structure of the network in rumor spreading is studied by analyzing the behavior of several global parameters such as reliability and efficiency. Our results show that while networks with homogeneous connectivity patterns reach a higher reliability, scale-free topologies need a less time to reach a steady state with respect the rumor.