A stochastic SIR epidemic on scale-free network with community structure

Zhang, Huiling; Guan, Zhi‐Hong; Li, Tao; Zhang, Xianhe; Zhang, Ding-Xue

doi:10.1016/j.physa.2012.10.016

Cited by 33 publications

(21 citation statements)

References 33 publications

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“…On the other hand, stochastic SIR models have been applied to simulate and predict the spatiotemporal diffusion of infectious diseases (Hufnagel et al, 2004;Cressie and Wikle, 2011;Ball and Sirl, 2012;Ji et al, 2012;de Souza et al, 2013;Zhang et al, 2013). This modeling, based on a consideration of stochastic differential equations, characterizes not only the spatiotemporal pattern of disease spread, but also the heteroscedastic variance pattern across space and time.…”

Section: Discussionmentioning

confidence: 99%

An online spatiotemporal prediction model for dengue fever epidemic inKaohsiung (Taiwan)

Angulo

Cheng

et al. 2014

Biometrical J

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The emergence and re-emergence of disease epidemics is a complex question that may be influenced by diverse factors, including the space-time dynamics of human populations, environmental conditions, and associated uncertainties. This study proposes a stochastic framework to integrate space-time dynamics in the form of a Susceptible-Infected-Recovered (SIR) model, together with uncertain disease observations, into a Bayesian maximum entropy (BME) framework. The resulting model (BME-SIR) can be used to predict space-time disease spread. Specifically, it was applied to obtain a space-time prediction of the dengue fever (DF) epidemic that took place in Kaohsiung City (Taiwan) during 2002. In implementing the model, the SIR parameters were continually updated and information on new cases of infection was incorporated. The results obtained show that the proposed model is rigorous to user-specified initial values of unknown model parameters, that is, transmission and recovery rates. In general, this model provides a good characterization of the spatial diffusion of the DF epidemic, especially in the city districts proximal to the location of the outbreak. Prediction performance may be affected by various factors, such as virus serotypes and human intervention, which can change the space-time dynamics of disease diffusion. The proposed BME-SIR disease prediction model can provide government agencies with a valuable reference for the timely identification, control, and prevention of DF spread in space and time.

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Section: Discussionmentioning

confidence: 99%

An online spatiotemporal prediction model for dengue fever epidemic inKaohsiung (Taiwan)

Angulo

Cheng

et al. 2014

Biometrical J

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“…Based on the SI (susceptible-infected) epidemic model, Shu et al numerically studied how weak ties (connect pairs of nodes belonging to different communities) influence epidemic dynamics [23]. Some scholars studied the SEAIR (susceptibleexposed-asymptomatically infected-symptomatically infectedrecovered) [32] and the stochastic SIR [31] epidemic model on scale-free networks with community structure. Bonaccorsi et al analyzed a continuous-time SIS model on a community structure network in which individuals that belong to different communities have different infecting probabilities [1].…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of epidemic spreading on community networks with heterogeneity

Jiang

Song

et al. 2018

Journal of Parallel and Distributed Computing

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h i g h l i g h t s• A modified community network model with heterogeneity among communities is proposed.• A mathematical epidemic model for each community is presented based on this network.• Study the effect of the location of initial infection node on epidemic spreading. • Study the impact of the heterogeneity among communities on epidemic spreading. a b s t r a c t A large number of real world networks exhibit community structure, and different communities may often possess heterogeneity. In this paper, considering the heterogeneity among communities, we construct a new community network model in which the communities show significant differences in average degree. Based on this heterogeneous community network, we propose a novel mathematical epidemic model for each community and study the epidemic dynamics in this network model. We find that the location of the initial infection node only affects the spreading velocity and barely influences the epidemic prevalence. And the epidemic threshold of entire network decreases with the increase of heterogeneity among communities. Moreover, the epidemic prevalence increases with the increase of heterogeneity around the epidemic threshold, while the converse situation holds when the infection rate is much greater than the epidemic threshold. (B. Song). example, the severe acute respiratory syndrome (SARS) in 2003, the H1N1 influenza A virus in 2009, the H7N9 avian influenza virus in 2013, the Ebola virus in 2014 and the Middle East respiratory syndrome coronavirus (MERS-CoV) in 2015. The problem of epidemic spreading has gained great attention over the years and people want to predict the epidemic spread trend and take effective public health measures with limited vaccine supply. As the topology properties of networks have a profound impact on the dynamics of epidemic spreading, it is necessary to consider the effect of community structure on epidemic spreading. So far, a lot of results on epidemic dynamics in community networks have been obtained [12,14,16,29,30].To simulate the real network, many different kinds of community network models were constructed based on classical networks, and some individual behavior characteristics in real networks (such as random walk, long-range jump and awareness) were also taken into account. Liu and Hu studied the SIS (susceptible-infected-susceptible) dynamics on a random community network model with probability p (q) of intra-(inter-)

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“…Many mechanisms of complex networks such as spreading dynamics, cascading reactions, and network synchronization are highly affected by a tiny fraction of so-called important nodes [7]. Identifying the most important nodes or ranking the node importance by using the method of quantitative analysis in large scale networks is thus very significant, which allows us to better control rumor and disease spreading [8,9], design viral marketing strategies [10], rank the reputation of scientists and publications [11,12], optimize limited resource allocation [13], protect critical regions from intended attacks [14], etc.…”

Section: Introductionmentioning

confidence: 99%

Node Importance Ranking of Complex Networks with Entropy Variation

2017

Entropy

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The heterogeneous nature of a complex network determines the roles of each node in the network that are quite different. Mechanisms of complex networks such as spreading dynamics, cascading reactions, and network synchronization are highly affected by a tiny fraction of so-called important nodes. Node importance ranking is thus of great theoretical and practical significance. Network entropy is usually utilized to characterize the amount of information encoded in the network structure and to measure the structural complexity at the graph level. We find that entropy can also serve as a local level metric to quantify node importance. We propose an entropic metric, Entropy Variation, defining the node importance as the variation of network entropy before and after its removal, according to the assumption that the removal of a more important node is likely to cause more structural variation. Like other state-of-the-art methods for ranking node importance, the proposed entropic metric is also used to utilize structural information, but at the systematical level, not the local level. Empirical investigations on real life networks, the Snake Idioms Network, and several other well-known networks, demonstrate the superiority of the proposed entropic metric, notably outperforming other centrality metrics in identifying the top-k most important nodes.Entropy 2017, 19, 303 2 of 17 ranking important nodes make use of the structural information [6]. For more details about the above mentioned centralities, we refer to [6,29].Structural complexity is perhaps the most important property of a complex network [1]. Network entropy is usually utilized to characterize the amount of information encoded in the network structure and to measure the structural complexity [30]. Recently, considerable effort has focused on quantifying network complexity using entropy measures [31], and several entropic metrics have been proposed; to name a few, network connectivity entropy [32], cyclic entropy [33], mapping entropy [34], hotspot entropy [35], Riemannian-geometric entropy [36], and q-entropy [37]. These measures have been shown to be extremely successful in quantifying the level of organization encoded in structural features of networks.As was mentioned before, we often resort to network structural information for ranking node importance, while entropy can serve as a fundamental tool to capture the structural information of complex networks. However, to the best of our knowledge, there are seldom entropic metrics developed to measure node importance. Two recent exceptions are the Relative Entropy [38] and Expected Force [39]. Relative entropy [38] is proposed as an integrated evaluation approach for node importance, which generates an optimal solution from different individual centrality indices by linear programming. Thus relative entropy serves not as a direct metric for node importance ranking, but a hybrid approach for synthesizing the existing ones. Expected Force [39] is a node property derived from local network topology to depict the ...

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A stochastic SIR epidemic on scale-free network with community structure

Cited by 33 publications

References 33 publications

An online spatiotemporal prediction model for dengue fever epidemic inKaohsiung (Taiwan)

An online spatiotemporal prediction model for dengue fever epidemic inKaohsiung (Taiwan)

Modeling and analysis of epidemic spreading on community networks with heterogeneity

Node Importance Ranking of Complex Networks with Entropy Variation

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