Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity

Complexity of Government response to COVID-19 pandemic: a perspective of coupled dynamics on information heterogeneity and epidemic outbreak

This study aims at modeling the universal failure in preventing the outbreak of COVID-19 via real-world data from the perspective of complexity and network science. Through formalizing information heterogeneity and government intervention in the coupled dynamics of epidemic and infodemic spreading, first, we find that information heterogeneity and its induced variation in human responses significantly increase the complexity of the government intervention decision. The complexity results in a dilemma between the socially optimal intervention that is risky for the government and the privately optimal intervention that is safer for the government but harmful to the social welfare. Second, via counterfactual analysis against the COVID-19 crisis in Wuhan, 2020, we find that the intervention dilemma becomes even worse if the initial decision time and the decision horizon vary. In the short horizon, both socially and privately optimal interventions agree with each other and require blocking the spread of all COVID-19-related information, leading to a negligible infection ratio 30 days after the initial reporting time. However, if the time horizon is prolonged to 180 days, only the privately optimal intervention requires information blocking, which would induce a catastrophically higher infection ratio than that in the counterfactual world where the socially optimal intervention encourages early-stage information spread. These findings contribute to the literature by revealing the complexity incurred by the coupled infodemic-epidemic dynamics and information heterogeneity to the governmental intervention decision, which also sheds insight into the design of an effective early warning system against the epidemic crisis in the future.

Influential Spreader Identification in Complex Networks Based on Network Connectivity and Efficiency

Influential spreader identification is a vital research area in complex network theory, which has important influence on application and popularization. Each of the existing methods has its own advantages and disadvantages, and there are still various methods proposed to solve this issue. In this paper, we come up with a new centrality of influential spreader identification based on network connectivity and efficiency (CEC). The consequences of spreader deletion can be generally divided into two parts, one is that the connectivity of network topology is destroyed, and the other is that network’s performance is degraded, which makes the network unable to meet the functional requirement. Therefore, the relative changes of connectivity and efficiency of network before and after removing spreaders are used to present the influence of spreaders. We adopt susceptible-infected (SI) model, a well-known infectious disease model, to verify the effectiveness of CEC through the spreading ability simulation of spreaders in actual networks. And the simulation results demonstrate the superiority of CEC.

Dynamic Immunization Node Model for Complex Networks Based on Community Structure and Threshold

In the information age of big data, and increasingly large and complex networks, there is a growing challenge of understanding how best to restrain the spread of harmful information, for example, a computer virus. Establishing models of propagation and node immunity are important parts of this problem. In this article, a dynamic node immune model, based on the community structure and threshold (NICT), is proposed. First, a network model is established, which regards nodes carrying harmful information as new nodes in the network. The method of establishing the edge between the new node and the original node can be changed according to the needs of different networks. The propagation probability between nodes is determined by using community structure information and a similarity function between nodes. Second, an improved immune gain, based on the propagation probability of the community structure and node similarity, is proposed. The improved immune gain value is calculated for neighbors of the infected node at each time step, and the node is immunized according to the hand-coded parameter: immune threshold. This can effectively prevent invalid or insufficient immunization at each time step. Finally, an evaluation index, considering both the number of immune nodes and the number of infected nodes at each time step, is proposed. The immune effect of nodes can be evaluated more effectively. The results of network immunization experiments, on eight real networks, suggest that the proposed method can deliver better network immunization than several other well-known methods from the literature.

An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the corresponding deterministic model. When $ R_0 < 1 $, almost surely exponential extinction and $ p $-th moment exponential extinction of epidemics are proved by Razumikhin-Mao Theorem. Whereas, when $ R_0 > 1 $, the system is persistent in the mean under sufficiently weak noise intensities, which indicates that the disease will prevail. Finally, the main results are demonstrated by numerical simulations.

Identifying influential nodes: A new method based on network efficiency of edge weight updating

Identification of influential nodes in complex networks is an area of exciting growth since it can help us to deal with various problems. Furthermore, identifying important nodes can be used across various disciplines, such as disease, sociology, biology, engineering, just to name a few. Hence, how to identify influential nodes more accurately deserves further research. Traditional identification methods usually only focus on the local or global information of the network. However, only focusing on a part of the information in the network will lead to the loss of information, resulting in inaccurate results. In order to address this problem, an identification method based on network efficiency of edge weight updating is proposed, which can effectively incorporate both global and local information of the network. Our proposed method avoids the lack of information in the network and ensures the accuracy of the results as much as possible. Moreover, by introducing the iterative idea of weight updating, some dynamic information is also introduced into our proposed method, which is more convincing. Varieties of experiments have been carried out on 11 real-world data sets to demonstrate the effectiveness and superiority of our proposed method.

Re-Thinking the Role of Government Information Intervention in the COVID-19 Pandemic: An Agent-Based Modeling Analysis

The COVID-19 pandemic imposes new challenges on the capability of governments in intervening with the information dissemination and reducing the risk of infection outbreak. To reveal the complexity behind government intervention decision, we build a bi-layer network diffusion model for the information-disease dynamics that were intervened in and conduct a full space simulation to illustrate the trade-off faced by governments between information disclosing and blocking. The simulation results show that governments prioritize the accuracy of disclosed information over the disclosing speed when there is a high-level medical recognition of the virus and a high public health awareness, while, for the opposite situation, more strict information blocking is preferred. Furthermore, an unaccountable government tends to delay disclosing, a risk-averse government prefers a total blocking, and a low government credibility will discount the effect of information disclosing and aggravate the situation. These findings suggest that information intervention is indispensable for containing the outbreak of infectious disease, but its effectiveness depends on a complicated way on both external social/epidemic factors and the governments' internal preferences and governance capability, for which more thorough investigations are needed in the future.

Susceptible-Infected-Susceptible Epidemic Discrete Dynamic System Based on Tsallis Entropy

This investigation deals with a discrete dynamic system of susceptible-infected-susceptible epidemic (SISE) using the Tsallis entropy. We investigate the positive and maximal solutions of the system. Stability and equilibrium are studied. Moreover, based on the Tsallis entropy, we shall formulate a new design for the basic reproductive ratio. Finally, we apply the results on live data regarding COVID-19.

Heatmap centrality: A new measure to identify super-spreader nodes in scale-free networks

The identification of potential super-spreader nodes within a network is a critical part of the study and analysis of real-world networks. Motivated by a new interpretation of the "shortest path" between two nodes, this paper explores the properties of the heatmap centrality by comparing the farness of a node with the average sum of farness of its adjacent nodes in order to identify influential nodes within the network. As many real-world networks are often claimed to be scale-free, numerical experiments based upon both simulated and real-world undirected and unweighted scale-free networks are used to illustrate the effectiveness of the proposed "shortest path" based measure with regards to its CPU run time and ranking of influential nodes.

Immunization strategies in directed networks

Many complex systems can be modeled as directed networks, which can be regarded as a generalization of undirected networks. In this paper, epidemic dynamics and immunization strategies in directed networks are studied. First, a Susceptible-Infected-Susceptible (SIS) model on a directed network is established employing the mean-field method, and its dynamics and epidemic threshold of the network are studied. Then based on the continuous degree technique, namely, considering the degree of a node as a continuous variable, we propose a method to calculate the epidemic threshold of the immunized network. Besides, some immunization strategies, including optimal immunization, random immunization, combined targeted immunization, and combined acquaintance immunization, and three special networks are considered. Finally, through numerical analysis, all immunization strategies are simulated and compared on different types of networks. We find that the nodes with the largest product of in-degree and out-degree are the most worthy of being immunized.

Identifying Influential Nodes in Complex Networks Based on Local Effective Distance

With the rapid development of Internet technology, the social network has gradually become an indispensable platform for users to release information, obtain information, and share information. Users are not only receivers of information, but also publishers and disseminators of information. How to select a certain number of users to use their influence to achieve the maximum dissemination of information has become a hot topic at home and abroad. Rapid and accurate identification of influential nodes in the network is of great practical significance, such as the rapid dissemination, suppression of social network information, and the smooth operation of the network. Therefore, from the perspective of improving computational accuracy and efficiency, we propose an influential node identification method based on effective distance, named KDEC. By quantifying the effective distance between nodes and combining the position of the node in the network and its local structure, the influence of the node in the network is obtained, which is used as an indicator to evaluate the influence of the node. Through experimental analysis of a lot of real-world networks, the results show that the method can quickly and accurately identify the influential nodes in the network, and is better than some classical algorithms and some recently proposed algorithms.

Disease Transmission and Networks

While epidemiological models have traditionally assumed that diseases spread by the mass action principle, actual contact networks within social groups do not meet this assumption. Theoretical models have shown that disease dynamics could vary considerably under different types of contact networks, but these models face challenges in terms of their evaluation due to the difficulty of collecting empirical data. The honeybee colony with its elaborate social organization and large repertoire of diseases provides an ideal setting to explore how the structure of the contact network contributes to the transmission of a disease.

Transmission Dynamics of an SIS Model with Age Structure on Heterogeneous Networks

Infection age is often an important factor in epidemic dynamics. In order to realistically analyze the spreading mechanism and dynamical behavior of epidemic diseases, in this paper, a generalized disease transmission model of SIS type with age-dependent infection and birth and death on a heterogeneous network is discussed. The model allows the infection and recovery rates to vary and depend on the age of infection, the time since an individual becomes infected. We address uniform persistence and find that the model has the sharp threshold property, that is, for the basic reproduction number less than one, the disease-free equilibrium is globally asymptotically stable, while for the basic reproduction number is above one, a Lyapunov functional is used to show that the endemic equilibrium is globally stable. Finally, some numerical simulations are carried out to illustrate and complement the main results. The disease dynamics rely not only on the network structure, but also on an age-dependent factor (for some key functions concerned in the model).

Bayesian inference of spreading processes on networks

Infectious diseases are studied to understand their spreading mechanisms, to evaluate control strategies and to predict the risk and course of future outbreaks. Because people only interact with few other individuals, and the structure of these interactions influence spreading processes, the pairwise relationships between individuals can be usefully represented by a network. Although the underlying transmission processes are different, the network approach can be used to study the spread of pathogens in a contact network or the spread of rumours in a social network. We study simulated simple and complex epidemics on synthetic networks and on two empirical networks, a social/contact network in an Indian village and an online social network. Our goal is to learn simultaneously the spreading process parameters and the first infected node, given a fixed network structure and the observed state of nodes at several time points. Our inference scheme is based on approximate Bayesian computation, a likelihood-free inference technique. Our method is agnostic about the network topology and the spreading process. It generally performs well and, somewhat counter-intuitively, the inference problem appears to be easier on more heterogeneous network topologies, which enhances its future applicability to real-world settings where few networks have homogeneous topologies.

A tradeoff between the losses caused by computer viruses and the risk of the manpower shortage

This article addresses the tradeoff between the losses caused by a new virus and the size of the team for developing an antivirus against the virus. First, an individual-level virus spreading model is proposed to capture the spreading process of the virus before the appearance of its natural enemy. On this basis, the tradeoff problem is modeled as a discrete optimization problem. Next, the influences of different factors, including the infection force, the infection function, the available manpower, the alarm threshold, the antivirus development effort and the network topology, on the optimal team size are examined through computer simulations. This work takes the first step toward the tradeoff problem, and the findings are instructive to the decision makers of network security companies.

Social Network Clustering and the Spread of HIV/AIDS Among Persons Who Inject Drugs in 2 Cities in the Philippines

INTRODUCTION

The Philippines has seen rapid increases in HIV prevalence among people who inject drugs. We study 2 neighboring cities where a linked HIV epidemic differed in timing of onset and levels of prevalence. In Cebu, prevalence rose rapidly from below 1% to 54% between 2009 and 2011 and remained high through 2013. In nearby Mandaue, HIV remained below 4% through 2011 then rose rapidly to 38% by 2013.

OBJECTIVES

We hypothesize that infection prevalence differences in these cities may owe to aspects of social network structure, specifically levels of network clustering. Building on previous research, we hypothesize that higher levels of network clustering are associated with greater epidemic potential.

METHODS

Data were collected with respondent-driven sampling among men who inject drugs in Cebu and Mandaue in 2013. We first examine sample composition using estimators for population means. We then apply new estimators of network clustering in respondent-driven sampling data to examine associations with HIV prevalence.

RESULTS

Samples in both cities were comparable in composition by age, education, and injection locations. Dyadic needle-sharing levels were also similar between the 2 cities, but network clustering in the needle-sharing network differed dramatically. We found higher clustering in Cebu than Mandaue, consistent with expectations that higher clustering is associated with faster epidemic spread.

CONCLUSIONS

This article is the first to apply estimators of network clustering to empirical respondent-driven samples, and it offers suggestive evidence that researchers should pay greater attention to network structure's role in HIV transmission dynamics.

The impact of contact patterns on epidemic dynamics

In social networks, individuals have relationships with their neighbor nodes (acquaintance contacts) and also randomly contact other nodes without direct links (stranger contacts). However, these two types of contact patterns are rarely considered together. In this paper, we propose a modified SIS (Susceptible-Infected-Susceptible) model in which a node not only contacts neighbor nodes but also randomly contacts other nodes in the network. We implement the model on a scale-free network and study the influence of different types of contact patterns on epidemic dynamics as well as three possible strategies people adopt when disease outbreaks. The results show that a greater preference for acquaintance contacts makes a disease outbreak less likely. Moreover, the best protective strategy to control the disease is to adjust both the contact number and the contact pattern. In addition, the epidemic is more likely to be controlled when individuals take more information into consideration.

Effective information spreading based on local information in correlated networks

Using network-based information to facilitate information spreading is an essential task for spreading dynamics in complex networks. Focusing on degree correlated networks, we propose a preferential contact strategy based on the local network structure and local informed density to promote the information spreading. During the spreading process, an informed node will preferentially select a contact target among its neighbors, basing on their degrees or local informed densities. By extensively implementing numerical simulations in synthetic and empirical networks, we find that when only consider the local structure information, the convergence time of information spreading will be remarkably reduced if low-degree neighbors are favored as contact targets. Meanwhile, the minimum convergence time depends non-monotonically on degree-degree correlation, and a moderate correlation coefficient results in the most efficient information spreading. Incorporating the local informed density information into contact strategy, the convergence time of information spreading can be further reduced, and be minimized by an moderately preferential selection.

Locating influential nodes via dynamics-sensitive centrality

With great theoretical and practical significance, locating influential nodes of complex networks is a promising issue. In this paper, we present a dynamics-sensitive (DS) centrality by integrating topological features and dynamical properties. The DS centrality can be directly applied in locating influential spreaders. According to the empirical results on four real networks for both susceptible-infected-recovered (SIR) and susceptible-infected (SI) spreading models, the DS centrality is more accurate than degree, k-shell index and eigenvector centrality.

Incorporating Contact Network Structure in Cluster Randomized Trials

Whenever possible, the efficacy of a new treatment is investigated by randomly assigning some individuals to a treatment and others to control, and comparing the outcomes between the two groups. Often, when the treatment aims to slow an infectious disease, clusters of individuals are assigned to each treatment arm. The structure of interactions within and between clusters can reduce the power of the trial, i.e. the probability of correctly detecting a real treatment effect. We investigate the relationships among power, within-cluster structure, cross-contamination via between-cluster mixing, and infectivity by simulating an infectious process on a collection of clusters. We demonstrate that compared to simulation-based methods, current formula-based power calculations may be conservative for low levels of between-cluster mixing, but failing to account for moderate or high amounts can result in severely underpowered studies. Power also depends on within-cluster network structure for certain kinds of infectious spreading. Infections that spread opportunistically through highly connected individuals have unpredictable infectious breakouts, making it harder to distinguish between random variation and real treatment effects. Our approach can be used before conducting a trial to assess power using network information, and we demonstrate how empirical data can inform the extent of between-cluster mixing.

EPIDEMIC SPREADING AND GLOBAL STABILITY OF A NEW SIS MODEL WITH DELAY ON HETEROGENEOUS NETWORKS

In this paper, we study a susceptible-infected-susceptible (SIS) model with time delay on complex heterogeneous networks. Here, the delay describes the incubation period in the vector population. We calculate the epidemic threshold by using a Lyapunov functional and some analytical methods, and find that adding delay increases the epidemic threshold. Then, we prove the global stability of disease-free and endemic equilibria by using the theory of functional differential equations. Furthermore, we show numerically that the epidemic threshold of the new model may change along with other factors, such as the infectivity function, the heterogeneity of the network, and the degrees of nodes. Finally, we find numerically that the delay can affect the convergence speed at which the disease reaches equilibria.

Mathematical and computational approaches to epidemic modeling: a comprehensive review

Mathematical and computational approaches are important tools for understanding epidemic spread patterns and evaluating policies of disease control. In recent years, epidemiology has become increasingly integrated with mathematics, sociology, management science, complexity science, and computer science. The cross of multiple disciplines has caused rapid development of mathematical and computational approaches to epidemic modeling. In this article, we carry out a comprehensive review of epidemic models to provide an insight into the literature of epidemic modeling and simulation. We introduce major epidemic models in three directions, including mathematical models, complex network models, and agent-based models. We discuss the principles, applications, advantages, and limitations of these models. Meanwhile, we also propose some future research directions in epidemic modeling.

A new closeness centrality measure via effective distance in complex networks

Closeness centrality (CC) measure, as a well-known global measure, is widely applied in many complex networks. However, the classical CC presents many problems for flow networks since these networks are directed and weighted. To address these issues, we propose an effective distance based closeness centrality (EDCC), which uses effective distance to replace conventional geographic distance and binary distance obtained by Dijkstra's shortest path algorithm. The proposed EDCC considers not only the global structure of the network but also the local information of nodes. And it can be well applied in directed or undirected, weighted or unweighted networks. Susceptible-Infected model is utilized to evaluate the performance by using the spreading rate and the number of infected nodes. Numerical examples simulated on four real networks are given to show the effectiveness of the proposed EDCC.

Epidemic spreading through direct and indirect interactions

In this paper we study the susceptible-infected-susceptible epidemic dynamics, considering a specialized setting where popular places (termed passive entities) are visited by agents (termed active entities). We consider two types of spreading dynamics: direct spreading, where the active entities infect each other while visiting the passive entities, and indirect spreading, where the passive entities act as carriers and the infection is spread via them. We investigate in particular the effect of selection strategy, i.e., the way passive entities are chosen, in the spread of epidemics. We introduce a mathematical framework to study the effect of an arbitrary selection strategy and derive formulas for prevalence, extinction probabilities, and epidemic thresholds for both indirect and direct spreading. We also obtain a very simple relationship between the extinction probability and the prevalence. We pay special attention to preferential selection and derive exact formulas. The analysis reveals that an increase in the diversity in the selection process lowers the epidemic thresholds. Comparing the direct and indirect spreading, we identify regions in the parameter space where the prevalence of the indirect spreading is higher than the direct one.

Epidemic spreading on hierarchical geographical networks with mobile agents

Hierarchical geographical traffic networks are critical for our understanding of scaling laws in human trajectories. Here, we investigate the susceptible-infected epidemic process evolving on hierarchical networks in which agents randomly walk along the edges and establish contacts in network nodes. We employ a metapopulation modeling framework that allows us to explore the contagion spread patterns in relation to multi-scale mobility behaviors. A series of computer simulations revealed that a shifted power-law-like negative relationship between the peak timing of epidemics τ 0 and population density, and a logarithmic positive relationship between τ 0 and the network size, can both be explained by the gradual enlargement of fluctuations in the spreading process. We employ a semi-analytical method to better understand the nature of these relationships and the role of pertinent demographic factors. Additionally, we provide a quantitative discussion of the efficiency of a border screening procedure in delaying epidemic outbreaks on hierarchical networks, yielding a rather limited feasibility of this mitigation strategy but also its non-trivial dependence on population density, infector detectability, and the diversity of the susceptible region. Our results suggest that the interplay between the human spatial dynamics, network topology, and demographic factors can have important consequences for the global spreading and control of infectious diseases. These findings provide novel insights into the combined effects of human mobility and the organization of geographical networks on spreading processes, with important implications for both epidemiological research and health policy.

Impact of media coverage on epidemic spreading in complex networks

An SIS network model incorporating the influence of media coverage on transmission rate is formulated and analyzed. We calculate the basic reproduction number R 0 by utilizing the local stability of the disease-free equilibrium. Our results show that the disease-free equilibrium is globally asymptotically stable and that the disease dies out if R 0 is below 1; otherwise, the disease will persist and converge to a unique positive stationary state. This result may suggest effective control strategies to prevent disease through media coverage and education activities in finite-size scale-free networks. Numerical simulations are also performed to illustrate our results and to give more insights into the dynamical process.

Identifying influential nodes in large-scale directed networks: the role of clustering

Identifying influential nodes in very large-scale directed networks is a big challenge relevant to disparate applications, such as accelerating information propagation, controlling rumors and diseases, designing search engines, and understanding hierarchical organization of social and biological networks. Known methods range from node centralities, such as degree, closeness and betweenness, to diffusion-based processes, like PageRank and LeaderRank. Some of these methods already take into account the influences of a node’s neighbors but do not directly make use of the interactions among it’s neighbors. Local clustering is known to have negative impacts on the information spreading. We further show empirically that it also plays a negative role in generating local connections. Inspired by these facts, we propose a local ranking algorithm named ClusterRank, which takes into account not only the number of neighbors and the neighbors’ influences, but also the clustering coefficient. Subject to the susceptible-infected-recovered (SIR) spreading model with constant infectivity, experimental results on two directed networks, a social network extracted from delicious.com and a large-scale short-message communication network, demonstrate that the ClusterRank outperforms some benchmark algorithms such as PageRank and LeaderRank. Furthermore, ClusterRank can also be applied to undirected networks where the superiority of ClusterRank is significant compared with degree centrality and k-core decomposition. In addition, ClusterRank, only making use of local information, is much more efficient than global methods: It takes only 191 seconds for a network with about nodes, more than 15 times faster than PageRank.

How human location-specific contact patterns impact spatial transmission between populations?

The structured-population model has been widely used to study the spatial transmission of epidemics in human society. Many seminal works have demonstrated the impact of human mobility on the epidemic threshold, assuming that the contact pattern of individuals is mixing homogeneously. Inspired by the recent evidence of location-related factors in reality, we introduce two categories of location-specific heterogeneous human contact patterns into a phenomenological model based on the commuting and contagion processes, which significantly decrease the epidemic threshold and thus favor the outbreak of diseases. In more detail, we find that a monotonic mode presents for the variance of disease prevalence in dependence on the contact rates under the destination-driven contact scenario; while under the origin-driven scenario, enhancing the contact rate counterintuitively weakens the disease prevalence in some parametric regimes. The inclusion of heterogeneity of human contacts is expected to provide valuable support to public health implications.

A bio-inspired methodology of identifying influential nodes in complex networks

How to identify influential nodes is a key issue in complex networks. The degree centrality is simple, but is incapable to reflect the global characteristics of networks. Betweenness centrality and closeness centrality do not consider the location of nodes in the networks, and semi-local centrality, leaderRank and pageRank approaches can be only applied in unweighted networks. In this paper, a bio-inspired centrality measure model is proposed, which combines the Physarum centrality with the K-shell index obtained by K-shell decomposition analysis, to identify influential nodes in weighted networks. Then, we use the Susceptible-Infected (SI) model to evaluate the performance. Examples and applications are given to demonstrate the adaptivity and efficiency of the proposed method. In addition, the results are compared with existing methods.

Effects of weak ties on epidemic predictability on community networks

Weak ties play a significant role in the structures and the dynamics of community networks. Based on the contact process, we study numerically how weak ties influence the predictability of epidemic dynamics. We first investigate the effects of the degree of bridge nodes on the variabilities of both the arrival time and the prevalence of disease, and find out that the bridge node with a small degree can enhance the predictability of epidemic spreading. Once weak ties are settled, the variability of the prevalence will display a complete opposite trend to that of the arrival time, as the distance from the initial seed to the bridge node or the degree of the initial seed increases. More specifically, the further distance and the larger degree of the initial seed can induce the better predictability of the arrival time and the worse predictability of the prevalence. Moreover, we discuss the effects of the number of weak ties on the epidemic variability. As the community strength becomes very strong, which is caused by the decrease of the number of weak ties, the epidemic variability will change dramatically. Compared with the case of the hub seed and the random seed, the bridge seed can result in the worst predictability of the arrival time and the best predictability of the prevalence.

Epidemic spreading on contact networks with adaptive weights

The heterogeneous patterns of interactions within a population are often described by contact networks, but the variety and adaptivity of contact strengths are usually ignored. This paper proposes a modified epidemic SIS model with a birth-death process and nonlinear infectivity on an adaptive and weighted contact network. The links' weights, named as 'adaptive weights', which indicate the intimacy or familiarity between two connected individuals, will reduce as the disease develops. Through mathematical and numerical analyses, conditions are established for population extermination, disease extinction and infection persistence. Particularly, it is found that the fixed weights setting can trigger the epidemic incidence, and that the adaptivity of weights cannot change the epidemic threshold but it can accelerate the disease decay and lower the endemic level. Finally, some corresponding control measures are suggested.

Epidemic spreading induced by diversity of agents' mobility

In this paper, we study the impact of the preference of an individual for public transport on the spread of infectious disease, through a quantity known as the public mobility. Our theoretical and numerical results based on a constructed model reveal that if the average public mobility of the agents is fixed, an increase in the diversity of the agents' public mobility reduces the epidemic threshold, beyond which an enhancement in the rate of infection is observed. Our findings provide an approach to improve the resistance of a society against infectious disease, while preserving the utilization rate of the public transportation system.

Epidemic variability in hierarchical geographical networks with human activity patterns

Recently, some studies have revealed that non-Poissonian statistics of human behaviors stem from the hierarchical geographical network structure. On this view, we focus on epidemic spreading in the hierarchical geographical networks and study how two distinct contact patterns (i.e., homogeneous time delay (HOTD) and heterogeneous time delay (HETD) associated with geographical distance) influence the spreading speed and the variability of outbreaks. We find that, compared with HOTD and null model, correlations between time delay and network hierarchy in HETD remarkably slow down epidemic spreading and result in an upward cascading multi-modal phenomenon. Proportionately, the variability of outbreaks in HETD has the lower value, but several comparable peaks for a long time, which makes the long-term prediction of epidemic spreading hard. When a seed (i.e., the initial infected node) is from the high layers of networks, epidemic spreading is remarkably promoted. Interestingly, distinct trends of variabilities in two contact patterns emerge: high-layer seeds in HOTD result in the lower variabilities, the case of HETD is opposite. More importantly, the variabilities of high-layer seeds in HETD are much greater than that in HOTD, which implies the unpredictability of epidemic spreading in hierarchical geographical networks.

Epidemic spreading in weighted networks: an edge-based mean-field solution

Weight distribution greatly impacts the epidemic spreading taking place on top of networks. This paper presents a study of a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation results show that the more homogeneous weight distribution leads to higher epidemic prevalence, which, unfortunately, could not be captured by the traditional mean-field approximation. This paper gives an edge-based mean-field solution for general weight distribution, which can quantitatively reproduce the simulation results. This method could be applied to characterize the nonequilibrium steady states of dynamical processes on weighted networks.

Effects of degree-biased transmission rate and nonlinear infectivity on rumor spreading in complex social networks

We introduce a generalized rumor spreading model and analytically investigate the spreading of rumors on scale-free (SF) networks. In the standard rumor spreading model, each node has an infectivity equal to its degree, and connectivity is uniform across all links. To generalize this model, we introduce an infectivity function that determines the number of simultaneous contacts that a given node (individual) may establish with its connected neighbors and a connectivity strength function (CSF) for the direct link between two connected nodes. These lead to a degree-biased propagation of rumors. For nonlinear functions, this generalization is reflected in the infectivity's exponent α and the CSF's exponent β. We show that, by adjusting exponents α and β, the epidemic threshold can be controlled. This feature is absent in the standard rumor spreading model. In addition, we obtain a critical threshold. We show that the critical threshold for our generalized model is greater than that of the standard model on a finite SF network. Theoretically, we show that β=-1 leads to a maximum spreading of rumors, and computation results on different networks verify our theoretical prediction. Also, we show that a smaller α leads to a larger spreading of rumors. Our results are interesting since we obtain these results regardless of the network topology and configuration.

Variability of contact process in complex networks

We study numerically how the structures of distinct networks influence the epidemic dynamics in contact process. We first find that the variability difference between homogeneous and heterogeneous networks is very narrow, although the heterogeneous structures can induce the lighter prevalence. Contrary to non-community networks, strong community structures can cause the secondary outbreak of prevalence and two peaks of variability appeared. Especially in the local community, the extraordinarily large variability in early stage of the outbreak makes the prediction of epidemic spreading hard. Importantly, the bridgeness plays a significant role in the predictability, meaning the further distance of the initial seed to the bridgeness, the less accurate the predictability is. Also, we investigate the effect of different disease reaction mechanisms on variability, and find that the different reaction mechanisms will result in the distinct variabilities at the end of epidemic spreading.

Evolution of scaling emergence in large-scale spatial epidemic spreading

Background

Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified.

Methodology/Principal Findings

In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence.

Conclusions/Significance

The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.

Staged progression model for epidemic spread on homogeneous and heterogeneous networks

In this paper, epidemic spread with the staged progression model on homogeneous and heterogeneous networks is studied. First, the epidemic threshold of the simple staged progression model is given. Then the staged progression model with birth and death is also considered. The case where infectivity is a nonlinear function of the nodes' degree is discussed, too. Finally, the analytical results are verified by numerical simulations.

Risk estimation of infectious diseases determines the effectiveness of the control strategy

Usually, whether to take vaccination or not is a voluntary decision, which is determined by many factors, from societal factors (such as religious belief and human rights) to individual preferences (including psychology and altruism). Facing the outbreaks of infectious diseases, different people often have different estimations on the risk of infectious diseases. So, some persons are willing to vaccinate, but other persons are willing to take risks. In this paper, we establish two different risk assessment systems using the technique of dynamic programming, and then compare the effects of the two different systems on the prevention of diseases on complex networks. One is that the perceived probability of being infected for each individual is the same (uniform case). The other is that the perceived probability of being infected is positively correlated to individual degrees (preferential case). We show that these two risk assessment systems can yield completely different results, such as, the effectiveness of controlling diseases, the time evolution of the number of infections, and so on.

Optimal contact process on complex networks

Contact processes on complex networks are a recent subject of study in nonequilibrium statistical physics and they are also important to applied fields such as epidemiology and computer and communication networks. A basic issue concerns finding an optimal strategy for spreading. We provide a universal strategy that, when a basic quantity in the contact process dynamics, the contact probability determined by a generic function of its degree W(k) , is chosen to be inversely proportional to the node degree, i.e., W(k) approximately k;{-1} , spreading can be maximized. Computation results on both model and real-world networks verify our theoretical prediction. Our result suggests the determining role played by small-degree nodes in optimizing spreading, in contrast to the intuition that hub nodes are important for spreading dynamics on complex networks.

Epidemic spreading in complex networks

The study of epidemic spreading in complex networks is currently a hot topic and a large body of results have been achieved. In this paper, we briefly review our contributions to this field, which includes the underlying mechanism of rumor propagation, the epidemic spreading in community networks, the influence of varying topology, and the influence of mobility of agents. Also, some future directions are pointed out.

Global behavior of epidemic transmission on heterogeneous networks via two distinct routes

In the study of epidemic spreading two natural questions are: whether the spreading of epidemics on heterogenous networks have multiple routes, and whether the spreading of an epidemic is a local or global behavior? In this paper, we answer the above two questions by studying the SIS model on heterogenous networks, and give the global conditions for the endemic state when two distinct routes with uniform rate of infection are considered. The analytical results are also verified by numerical simulations.

Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization

We examine epidemic thresholds for disease spread using susceptible-infected-susceptible models on scale-free networks with variable infectivity. Infectivity between nodes is modeled as a piecewise linear function of the node degree (rather than the less realistic linear transformation considered previously). With this nonlinear infectivity, we derive conditions for the epidemic threshold to be positive. The effects of various immunization schemes including ring and targeted vaccination are studied and compared. We find that both targeted and ring immunization strategies compare favorably to a proportional scheme in terms of effectiveness.

Fast algorithm for successive computation of group betweenness centrality

In this paper, we propose a method for rapid computation of group betweenness centrality whose running time (after preprocessing) does not depend on network size. The calculation of group betweenness centrality is computationally demanding and, therefore, it is not suitable for applications that compute the centrality of many groups in order to identify new properties. Our method is based on the concept of path betweenness centrality defined in this paper. We demonstrate how the method can be used to find the most prominent group. Then, we apply the method for epidemic control in communication networks. We also show how the method can be used to evaluate distributions of group betweenness centrality and its correlation with group degree. The method may assist in finding further properties of complex networks and may open a wide range of research opportunities.