具有非均匀传输和抗攻击差异的网络病毒传播模型

针对实际网络中节点存在抗攻击差异以及边的非均匀传输等情况,基于平均场理论,提出具有抗攻击差异和非均匀传输特性的网络病毒传播平均场SIR模型.该模型中,通过引入脆弱性函数和传输函数,分别描述节点的抗攻击差异以及边的非均匀传输能力.通过对所提模型的分析,得到传播阈值的理论结果.理论分析和仿真表明,节点的抗攻击差异以及边的非均匀传输,都可导致出现正的传播阈值,使得病毒传播风险有效降低.     

Epidemic thresholds in a heterogenous population with competing strains

Among many epidemic models,one epidemic disease may transmit with the existence of other pathogens or other strains from the same pathogen. In this paper,we consider the case where all of the strains obey the susceptible-infected-susceptible mechanism and compete with each other at the expense of common susceptible individuals. By using the heterogenous mean-field approach,we discuss the epidemic threshold for one of two strains. We confirm the existence of epidemic threshold in both finite and infinite populations subject to underlying epidemic transmission. Simulations in the Barabasi-Albert (BA) scale-free networks are in good agreement with the analytical results.     

Discrete Stochastic Modeling for Epidemics in Networks

In this paper, we construct a microscopic mechanism for the epidemic processes in heterogeneous populations, which contains two basic assumptions: all edges of the network are broken and reconnected at every time step among the epidemic process; the probability of randomly chosen two half-edges to make a pair is identical. We define the stochastic epidemic process and get the epidemic distributions numerically according to the transmission probability λ. Two different phases are observed, which means the onset of phase transition, and the threshold value is very small. Under the thermodynamic limit, the process can be approximated by a deterministic dynamical system. About this deterministic system, we get the analytical threshold value, which is consistent with the numerical results of the epidemic distributions.     

具有局部结构的增长无标度网络中传染病传播机制研究

为了研究人群中的一些基本的社会关系结构,如家庭、室友、同事等,对传染病传播过程的影响机制,本文建立了一个具有局部结构的增长无标度网络模型.研究表明,局部结构的引入使得该网络模型能够同时再现社会网络的两个重要特征：节点度分布的不均匀性以及节点度之间的相关性.首先,该网络的节点度和局部结构度均服从幂律分布,且度分布指数依赖于局部结构的大小.此外,局部结构的存在还导致网络节点度之间具有正相关特性,而这种正相关正是社会网络所特有的一个重要特性.接着,通过理论分析和数值模拟,我们进一步研究了该网络结构对易感者-感染 关键词： 复杂网络 无标度网络 局部结构 传染病建模     

Epidemic threshold and phase transition in scale-free networks with asymmetric infection

We study the SIS epidemic dynamics on scale-freeweighted networks with asymmetric infection, by both analysis andnumerical simulations, with focus on the epidemic threshold aswell as critical behaviors. It is demonstrated that the asymmetryof infection plays an important role: we could redistribute theasymmetry to balance the degree heterogeneity of the network andthen to restore the epidemic threshold to a fnite value. On theother hand, we show that the absence of the epidemic threshold isnot so bad as commented previously since the prevalence grows veryslowly in this case and one could only protect a few vertices toprevent the diseases propagation.     

Quantifying the transmission potential of pandemic influenza

This article reviews quantitative methods to estimate the basic reproduction number of pandemic influenza, a key threshold quantity to help determine the intensity of interventions required to control the disease. Although it is difficult to assess the transmission potential of a probable future pandemic, historical epidemiologic data is readily available from previous pandemics, and as a reference quantity for future pandemic planning, mathematical and statistical analyses of historical data are crucial. In particular, because many historical records tend to document only the temporal distribution of cases or deaths (i.e. epidemic curve), our review focuses on methods to maximize the utility of time-evolution data and to clarify the detailed mechanisms of the spread of influenza.

First, we highlight structured epidemic models and their parameter estimation method which can quantify the detailed disease dynamics including those we cannot observe directly. Duration-structured epidemic systems are subsequently presented, offering firm understanding of the definition of the basic and effective reproduction numbers. When the initial growth phase of an epidemic is investigated, the distribution of the generation time is key statistical information to appropriately estimate the transmission potential using the intrinsic growth rate. Applications of stochastic processes are also highlighted to estimate the transmission potential using similar data. Critically important characteristics of influenza data are subsequently summarized, followed by our conclusions to suggest potential future methodological improvements.     

Epidemic spreading with nonlinear infectivity in weighted scale-free networks

In this paper, we investigate the epidemic spreading for the SIR model in weighted scale-free networks with the nonlinear infectivity and weighted transmission rate. Concretely, we introduce the infectivity exponent α and the weight exponent β into the epidemic system, then examine the impact of α and β on the epidemic spreading. We show that one can adjust the values of α and β to rebuild a nonzero finite epidemic threshold. Furthermore, we also find the infectivity exponent α has a stronger effect not only on the epidemic threshold, but also on the epidemic prevalence. In addition, it is also interesting to see that the absence of the epidemic threshold appears not very dejected, since the prevalence grows much more slowly as the transmission rate λ increases.     

Threshold effects for two pathogens spreading on a network

Diseases spread through host populations over the networks of contacts between individuals and a number of results about this process have been derived in recent years by exploiting connections between epidemic processes and bond percolation on networks. Here we investigate the case of two pathogens in a single population, which has been the subject of recent interest among epidemiologists. We demonstrate that two pathogens competing for the same hosts can both spread through a population only for intermediate values of the bond occupation probability that lie above the classic epidemic threshold and below a second higher value, which we call the coexistence threshold, corresponding to a distinct topological phase transition in networked systems.     

Finite size effects in epidemic spreading: the problem of overpopulated systems

In this paper we analyze the impact of network size on the dynamics of epidemic spreading. In particular, we investigate the pace of infection in overpopulated systems. In order to do that, we design a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step, which can serve as a model for sexually transmitted diseases spreading in some student communes. Because of the highly discrete character of the process, the analysis cannot use the continuous approximation widely exploited for most models. Using a discrete approach, we investigate the epidemic threshold and the quasi-stationary distribution. The main results are two theorems about the mixing time for the process: it scales like the logarithm of the network size and it is proportional to the inverse of the distance from the epidemic threshold.     

Disease spreading in structured scale-free networks

We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the network are unbounded whether the epidemic threshold exists strongly depends on the initial density of infected individuals and the type of epidemiological model considered. Analytical arguments are provided in order to account for the observed behavior. We conclude that the peculiar topological features of this network and the absence of small-world properties determine the dynamics of epidemic spreading. Received 16 October 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: yamir@ictp.trieste.it     

Magnetic and quantum entanglement properties of the distorted diamond chain model for azurite

On the basis of experimental data on interactions between humans we have investigated the process of epidemic spreading in a social network. We found that the distribution of the number of contacts maintained in one day is exponential. Data on frequency and duration of interpersonal interactions are presented. They allow us to simulate the spread of droplet-/-air-borne infections and to investigate the influence of human dynamics on the epidemic spread. Specifically, we investigated the influence of the distribution of frequency and duration of those contacts on magnitude, epidemic threshold and peak timing of epidemics propagating in respective networks. It turns out that a large increase in the magnitude of an epidemic and a decrease in epidemic threshold are visible if and only if both are taken into account. We have found that correlation between contact frequency and duration strongly influences the effectiveness of control measures like mass immunization campaigns.     

Disease spreading on fitness-rewired complex networks

As people travel, human contact networks may change topologically from time to time. In this paper, we study the problem of epidemic spreading on this kind of dynamic network, specifically the one in which the rewiring dynamics of edges are carried out to preserve the degree of each node (called fitness rewiring). We also consider the adaptive rewiring of edges, which encourages disconnections from and discourages connections to infected nodes and eventually leads to the isolation of the infected from the susceptible with only a small number of links between them. We find that while the threshold of epidemic spreading remains unchanged and prevalence increases in the fitness rewiring dynamics, meeting of the epidemic threshold is delayed and prevalence is reduced (if adaptive dynamics are included). To understand these different behaviors, we introduce a new measure called the “mean change of effective links” and find that creation and deletion of pathways for pathogen transmission are the dominant factors in fitness and adaptive rewiring dynamics, respectively.     

Scaling behavior of threshold epidemics

We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease from infected individuals, while infected ones recover from the disease at a constant rate and are never infected again. Our focus is the behavior at the epidemic threshold where the rates of the infection and recovery processes balance. In the infinite population limit, we establish analytically scaling rules for the time-dependent distribution functions that characterize the sizes of the infected and the recovered sub-populations. Using heuristic arguments, we also obtain scaling laws for the size and duration of the epidemic outbreaks as a function of the total population. We perform numerical simulations to verify the scaling predictions and discuss the consequences of these scaling laws for near-threshold epidemic outbreaks.     

Mathematical models to characterize early epidemic growth: A review

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014–2015 Ebola epidemic in West Africa.     

Epidemics spread in heterogeneous populations

Individuals building populations are subject to variability. This variability affects progress of epidemic outbreaks, because individuals tend to be more or less resistant. Individuals also differ with respect to their recovery rate. Here, properties of the SIR model in inhomogeneous populations are studied. It is shown that a small change in model’s parameters, e.g. recovery or infection rate, can substantially change properties of final states which is especially well-visible in distributions of the epidemic size. In addition to the epidemic size and radii distributions, the paper explores first passage time properties of epidemic outbreaks.     

Contagion dynamics on adaptive multiplex networks with awareness-dependent rewiring

Over the last few years, the interplay between contagion dynamics of social influences (e.g., human awareness, risk perception, and information dissemination) and biological infections has been extensively investigated within the framework of multiplex networks. The vast majority of existing multiplex network spreading models typically resort to heterogeneous mean-field approximation and microscopic Markov chain approaches. Such approaches usually manifest richer dynamical properties on multiplex networks than those on simplex networks; however, they fall short of a subtle analysis of the variations in connections between nodes of the network and fail to account for the adaptive behavioral changes among individuals in response to epidemic outbreaks. To transcend these limitations, in this paper we develop a highly integrated effective degree approach to modeling epidemic and awareness spreading processes on multiplex networks coupled with awareness-dependent adaptive rewiring. This approach keeps track of the number of nearest neighbors in each state of an individual; consequently, it allows for the integration of changes in local contacts into the multiplex network model. We derive a formula for the threshold condition of contagion outbreak. Also, we provide a lower bound for the threshold parameter to indicate the effect of adaptive rewiring. The threshold analysis is confirmed by extensive simulations. Our results show that awareness-dependent link rewiring plays an important role in enhancing the transmission threshold as well as lowering the epidemic prevalence. Moreover, it is revealed that intensified awareness diffusion in conjunction with enhanced link rewiring makes a greater contribution to disease prevention and control. In addition, the critical phenomenon is observed in the dependence of the epidemic threshold on the awareness diffusion rate, supporting the metacritical point previously reported in literature. This work may shed light on understanding of the interplay between epidemic dynamics and social contagion on adaptive networks.     

Modelling the effect of heterogeneous vaccination on metapopulation epidemic dynamics

Vaccination as an epidemic control strategy has a significant effect on epidemic spreading. In this paper, we propose a novel epidemic spreading model on metapopulation networks to study the impact of heterogeneous vaccination on epidemic dynamics, where nodes represent geographical areas and links connecting nodes correspond to human mobility between areas. Using a mean-field approach, we derive the theoretical spreading threshold revealing a non-trivial dependence on the heterogeneity of vaccination. Extensive Monte Carlo simulations validate the theoretical threshold and also show the complex temporal epidemic behaviours above the threshold.     

A Weighted Configuration Model and Inhomogeneous Epidemics

A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An expression for the threshold for the appearance of a giant component in the resulting graph is derived using results on multi-type branching processes. The same technique also gives an expression for the basic reproduction number for an epidemic on the graph where the probability that a certain edge is used for transmission is a function of the edge weight (reflecting how closely ‘connected’ the corresponding vertices are). It is demonstrated that, if vertices with large degree tend to have large (small) weights on their edges and if the transmission probability increases with the edge weight, then it is easier (harder) for the epidemic to take off compared to a randomized epidemic with the same degree and weight distribution. A recipe for calculating the probability of a large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the model is fitted to three empirical weighted networks of importance for the spread of contagious diseases and it is shown that R ₀ can be substantially over- or underestimated if the correlation between degree and weight is not taken into account.     

异质自适应网络中的核心-边缘结构及其对疾病传播的抑制作用

节点属性异质自适应网络中疾病传播的研究表明节点属性异质性可以很大程度上增大传播阈值, 并且自组织形成一个更鲁棒的度异质网络结构. 本文从数值模拟方面研究鲁棒的度分布异质结构的自组织形成过程, 分析发现核心-边缘结构的形成才是导致传播阈值增大的根本原因. 鉴于此, 提出一种重连策略, 能够促进核心-边缘结构的形成, 从而达到增大传播阈值的目的. 这不仅有助于深入认识节点属性异质自适应网络中的流行病传播过程, 而且为疾病传播控制策略的提出提供了新思路.     

Electrophysical and acoustic properties of magnetic elastomers structured by an external magnetic field

Magnetoactive elastomers are promising for use in designing of magnetically operated devices for signal processing and sensors. The results from studying the electrophysical and acoustic properties of new magnetoactive elastomers structured by a nonuniform magnetic field are presented. It is shown that the prestructuring of the magnetic disperse filler by a magnetic field during composite synthesis substantially improves the coefficient of the transmission of electromagnetic radiation through the sample. The effect gets stronger as the mass fraction of filler increases. As the filler concentration grows, the transmission coefficient falls by 50%, and the ref lection coefficient grows by a factor of 150%. The longitudinal elastic modulus and the density vary within the ranges of 1.4–1.8 GPa and 2485–3362 kg m^–3, respectively, depending on the magnetic filler concentration and the sample’s structuring. The obtained results demonstrate the potential of usinf structured magnetoactive elastomers as radar absorbing materials.