Path-Based Epidemic Spreading in Networks

Chai, Wei Koong; Pavlou, George

doi:10.1109/tnet.2016.2594382

Cited by 19 publications

(13 citation statements)

References 51 publications

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“…This is logical since we get higher γ 1 when c n,m assumes larger values (see Theorem 2 in [25]) which means there is higher volume of agents traversing nodes (and thus, passing on the contagion) within the network.…”

Section: Network As a Wholementioning

confidence: 88%

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Modelling Spreading Process Induced by Agent Mobility in Complex Networks

Chai

2018

IEEE Trans. Netw. Sci. Eng.

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Abstract-Most conventional epidemic models assume contact-based contagion process. We depart from this assumption and study epidemic spreading process in networks caused by agents acting as carrier of infection. These agents traverse from origins to destinations following specific paths in a network and in the process, infecting the sites they travel across. We focus our work on the Susceptible-Infected-Removed (SIR) epidemic model and use continuous-time Markov chain analysis to model the impact of such agent mobility induced contagion mechanics by taking into account the state transitions of each node individually, as oppose to most conventional epidemic approaches which usually consider the mean aggregated behavior of all nodes. Our approach makes one mean field approximation to reduce complexity from exponential to polynomial. We study both network-wide properties such as epidemic threshold as well as individual node vulnerability under such agent assisted infection spreading process. Furthermore, we provide a first order approximation on the agents' vulnerability since infection is bi-directional. We compare our analysis of spreading process induced by agent mobility against contact-based epidemic model via a case study on London Underground network, the second busiest metro system in Europe, with real dataset recording commuters' activities in the system. We highlight the key differences in the spreading patterns between the contact-based vs. agent assisted spreading models. Specifically, we show that our model predicts greater spreading radius than conventional contact-based model due to agents' movements. Another interesting finding is that, in contrast to contact-based model where nodes located more centrally in a network are proportionally more prone to infection, our model shows no such strict correlation as in our model, nodes may not be highly susceptible even located at the heart of the network and vice versa.

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Section: Network As a Wholementioning

confidence: 88%

“…Spreading is now dictated by the amount of activity and mobility pattern of the agents. Our approach takes the analytical framework studied in [12] [25] as the starting point. In our model, we create an infection characterization matrix that allows us to draw insights into the behavior of the epidemic.…”

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confidence: 99%

Modelling Spreading Process Induced by Agent Mobility in Complex Networks

Chai

2018

IEEE Trans. Netw. Sci. Eng.

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“…The statistic topology models are generally based on undirected networks. However, there is an intrinsic directionality in the propagation in specific types of dynamics, e.g., infectious disease spreading [24] and information transmission [25]. Directed networks, sets of vertices, and a collection of directed edges that connect pairs of ordered vertices are useful to represent specific transmissions with intrinsic directionality in the propagation [14].…”

Section: Related Workmentioning

confidence: 99%

Group-Based Susceptible-Infectious-Susceptible Model in Large-Scale Directed Networks

Wang

Song

et al. 2019

Security and Communication Networks

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Epidemic models trade the modeling accuracy for complexity reduction. This paper proposes to group vertices in directed graphs based on connectivity and carries out epidemic spread analysis on the group basis, thereby substantially reducing the modeling complexity while preserving the modeling accuracy. A group-based continuous-time Markov SIS model is developed. The adjacency matrix of the network is also collapsed according to the grouping, to evaluate the Jacobian matrix of the group-based continuous-time Markov model. By adopting the mean-field approximation on the groups of nodes and links, the model complexity is significantly reduced as compared with previous topological epidemic models. An epidemic threshold is deduced based on the spectral radius of the collapsed adjacency matrix. The epidemic threshold is proved to be dependent on network structure and interdependent of the network scale. Simulation results validate the analytical epidemic threshold and confirm the asymptotical accuracy of the proposed epidemic model.

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“…Moreover, discretetime models assume a certain time interval between when a vulnerable node is exposed to an infection and when it becomes an infected node, which is denoted by t in this paper. On the other hand, continuous-time epidemic models treat time as a continuum and have been applied in [6], [14], [24], [27], [29]. Some continuous-time epidemic models can be regarded as special cases of discrete-time models when…”

Section: Introductionmentioning

confidence: 99%

“…As shown in this paper, a widely used continuous-time epidemic model [6], [14], [24] ignores time intervals, assumes spatial independence among nodes, and applies linearization in the model (See Section II-E).…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time vs. Continuous-Time Epidemic Models in Networks

Chen

2019

IEEE Access

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Epidemic models have been a widely used mathematical tool in network security and social networks to study malware propagation and information dissemination. However, the relationships and the differences of discrete-time and continuous-time epidemic models in networks have not been systematically studied yet. In this paper, we focus on the susceptible-infectious model and attempt to connect and compare different discrete-time and continuous-time epidemic models through both theoretical analysis and empirical verification. We find that epidemic models can be distinguished based on whether a model considers the following three key factors: time intervals, spatial dependence among nodes, and linearization. We theoretically and empirically show that ignoring time intervals, assuming spatial independence among nodes, or applying linearization can cause a model to possibly over-predict the propagation speed of an epidemic. Especially, we discover that a widely used continuous-time epidemic model cannot accurately characterize the spread of the actual epidemic by ignoring both time intervals and spatial dependence among nodes. INDEX TERMS Epidemic models, susceptible-infectious (SI) model, discrete-time epidemic models, continuous-time epidemic models. ZESHENG CHEN (S'03-M'07-SM'16) received the M.S. and Ph.D. degrees from the Georgia Institute of Technology, in 2005 and 2007, respectively. He is currently an Assistant Professor with the Department of Computer Science, Purdue University Fort Wayne. His current research interests include network security, the Internet of Things, social networks, and performance evaluation of communication networks.

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Path-Based Epidemic Spreading in Networks

Cited by 19 publications

References 51 publications

Modelling Spreading Process Induced by Agent Mobility in Complex Networks

Modelling Spreading Process Induced by Agent Mobility in Complex Networks

Group-Based Susceptible-Infectious-Susceptible Model in Large-Scale Directed Networks

Discrete-Time vs. Continuous-Time Epidemic Models in Networks

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