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Epidemics on a Stochastic Model of Temporal Network

  • Luis E. C. Rocha
  • Adeline Decuyper
  • Vincent D. Blondel
Chapter
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Abstract

This chapter presents a simple and intuitive stochastic model of a temporal network and investigate how a simulated infection co-evolves with the temporal structures, focusing on the growth dynamics of the epidemics. The model assumes no underlying topological structure and is only constrained by the time between two consecutive events of vertex activation, hereafter called vertex inter-event time. The network model consists of random activations of a vertex according to a pre-defined vertex inter-event time distribution. The vertices active at a given time are randomly connected in pairs during one time unit. The link is then destroyed and the vertices set to the inactive state. The infection event occurs through this link if one of the vertices is in an infective state. This model has been studied by using a susceptible infective dynamics with one (SI) and two (SII) infective stages. The first dynamics is motivated for being an upper limit case, where once infected, the vertex continues infecting at every contact. The second dynamics is more realistic and corresponds to a model of HIV spreading including an acute (high infectivity) and chronic (low infectivity) stages of infection with different periods. If the second stage is set to zero in the SII model, we recover the susceptible infected recovered (SIR).

Notes

Acknowledgement

LECR is beneficiary of a FSR incoming postdoctoral fellowship of the Académie universitaire Louvain, co-funded by the Marie Curie Actions of the European Commission. AD is a research fellow with the Fonds National de la Recherche Scientifique (FRS-FNRS). Computational resources have been provided by the supercomputing facilities of the Université catholique de Louvain (CISM/UCL) and the Consortium des Équipements de Calcul Intensif en Fédération Wallonie Bruxelles (CECI) funded by FRS-FNRS.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Luis E. C. Rocha
    • 1
  • Adeline Decuyper
    • 1
  • Vincent D. Blondel
    • 1
  1. 1.Department of Mathematical EngineeringUniversité catholique de LouvainLouvain-la-NeuveBelgium

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