Staged progression model for epidemic spread on homogeneous and heterogeneous networks

Zhang, Haifeng; Small, Michael; Fu, Xinchu

doi:10.1007/s11424-011-8252-8

Cited by 17 publications

(7 citation statements)

References 19 publications

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“…So the model of congestion propagation in different stage should take varied factors into account. In this paper, we focus on the congestion propagation of departure aircraft from airport using multistage and multievent models [32,33]. The assumption is that propagation characteristics resulting from a particular "event" and at a particular "stage" manifest a distinct "spectrum" (defined as the evolution of congestion clusters with time in a given airport).…”

Section: Introductionmentioning

confidence: 99%

Modeling Congestion Propagation in Multistage Schedule within an Airport Network

Dai

Tian

et al. 2018

Journal of Advanced Transportation

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In order to alleviate flight delay it is important to understand how air traffic congestion evolves or propagates. In this context, this paper focusses on the aggravation of airport congestion by the accumulation of delayed departure flights. We start by applying a heterogeneous network model that takes congestion connection/degree into consideration to predict departure congestion clusters. This is on the basis of the fact that, from a micro perspective, the connection between congestion and discrete clusters can be embodied in models. However, the results show prediction to be of high accuracy and time consuming due to the complexities in capturing the connection in congested flights. The problem of being highly time consuming is resolved in this paper by improving the models by stages. Stage partitioning based on the variation of delay clusters is similar to the typical infectious cycle. For heterogeneous networks the model can describe the congestion propagation and its causes at the different stages of operation. If the connection between flights is homogeneous, the model can describe a more indicative process or trend of congestion propagation. In particular, for single source congestion, the simplified multistage models enable short-term prediction to be fast. Furthermore, for the controllers, the accuracy of prediction using simplified models can be acceptable and the speed on the prediction is significantly increased. The simplified models can help controllers to understand congestion propagation characteristics at different stages of operation, make a fast and short-term prediction of congestion clusters, and facilitate the formulation of traffic control strategies.

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Section: Introductionmentioning

confidence: 99%

Modeling Congestion Propagation in Multistage Schedule within an Airport Network

Dai

Tian

et al. 2018

Journal of Advanced Transportation

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“…It is found that the constant change of the network topology which caused by the individuals' birth and death enhances the epidemic incidence and reduces the epidemic threshold. Zhang et al considered the epidemic thresholds for a staged progression model with birth and death on homogeneous and heterogeneous networks respectively [6]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of epidemic spreading on community network with node's birth and death

Jiang

2016

The Journal of China Universities of Posts and Telecommunicatio

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“…However, there is little literature about the infectious period distribution problems based on networks. Zhang et al in 2011 proposed a susceptibleinfected-susceptible staged progression and different infectivity models on different complex networks [12], where the infectious period follows a gamma distribution. Zager and Verghese in 2009 established a discrete differential equation to present an arbitrarily distributed infectious period [13].…”

Section: Introductionmentioning

confidence: 99%

Global Dynamics of Infectious Disease with Arbitrary Distributed Infectious Period on Complex Networks

Zhang

Song

Sun

et al. 2014

Discrete Dynamics in Nature and Society

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Most of the current epidemic models assume that the infectious period follows an exponential distribution. However, due to individual heterogeneity and epidemic diversity, these models fail to describe the distribution of infectious periods precisely. We establish a SIS epidemic model with multistaged progression of infectious periods on complex networks, which can be used to characterize arbitrary distributions of infectious periods of the individuals. By using mathematical analysis, the basic reproduction numberR0for the model is derived. We verify that theR0depends on the average distributions of infection periods for different types of infective individuals, which extend the general theory obtained from the single infectious period epidemic models. It is proved that ifR0<1, then the disease-free equilibrium is globally asymptotically stable; otherwise the unique endemic equilibrium exists such that it is globally asymptotically attractive. Finally numerical simulations hold for the validity of our theoretical results is given.

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Staged progression model for epidemic spread on homogeneous and heterogeneous networks

Cited by 17 publications

References 19 publications

Modeling Congestion Propagation in Multistage Schedule within an Airport Network

Modeling Congestion Propagation in Multistage Schedule within an Airport Network

Modeling and analysis of epidemic spreading on community network with node's birth and death

Global Dynamics of Infectious Disease with Arbitrary Distributed Infectious Period on Complex Networks

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