IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v107y2003i2p233-268.html
   My bibliography  Save this article

The great circle epidemic model

Author

Listed:
  • Ball, Frank
  • Neal, Peter

Abstract

We consider a stochastic model for the spread of an epidemic among a population of n individuals that are equally spaced around a circle. Throughout its infectious period, a typical infective, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently and uniformly according to a contact distribution centred on i. The asymptotic situation in which the local contact distribution converges weakly as n-->[infinity] is analysed. A branching process approximation for the early stages of an epidemic is described and made rigorous as n-->[infinity] by using a coupling argument, yielding a threshold theorem for the model. A central limit theorem is derived for the final outcome of epidemics that take off, by using an embedding representation. The results are specialised to the case of a symmetric, nearest-neighbour local contact distribution.

Suggested Citation

  • Ball, Frank & Neal, Peter, 2003. "The great circle epidemic model," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 233-268, October.
    • Handle: RePEc:eee:spapps:v:107:y:2003:i:2:p:233-268
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(03)00074-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ball, Frank & Donnelly, Peter, 1995. "Strong approximations for epidemic models," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 1-21, January.
    2. Cristopher Moore & M. E. J. Newman, 2000. "Epidemics and Percolation in Small-World Networks," Working Papers 00-01-002, Santa Fe Institute.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ganjeh-Ghazvini, Mostafa & Masihi, Mohsen & Ghaedi, Mojtaba, 2014. "Random walk–percolation-based modeling of two-phase flow in porous media: Breakthrough time and net to gross ratio estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 214-221.
    2. Sadeghnejad, S. & Masihi, M. & King, P.R., 2013. "Dependency of percolation critical exponents on the exponent of power law size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6189-6197.
    3. Pan, Ya-Nan & Lou, Jing-Jing & Han, Xiao-Pu, 2014. "Outbreak patterns of the novel avian influenza (H7N9)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 265-270.
    4. Greg Morrison & L Mahadevan, 2012. "Discovering Communities through Friendship," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    5. Andrea Giovannetti, 2012. "Financial Contagion in Industrial Clusters: A Dynamical Analysis and Network Simulation," Department of Economics University of Siena 654, Department of Economics, University of Siena.
    6. Floortje Alkemade & Carolina Castaldi, 2005. "Strategies for the Diffusion of Innovations on Social Networks," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 3-23, February.
    7. Qin, Yang & Zhong, Xiaoxiong & Jiang, Hao & Ye, Yibin, 2015. "An environment aware epidemic spreading model and immune strategy in complex networks," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 206-215.
    8. Velarde, Carlos & Robledo, Alberto, 2021. "Statistical mechanical model for growth and spread of contagions under gauged population confinement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    9. Simon, Matthieu, 2020. "SIR epidemics with stochastic infectious periods," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4252-4274.
    10. I. Vieira & R. Cheng & P. Harper & V. Senna, 2010. "Small world network models of the dynamics of HIV infection," Annals of Operations Research, Springer, vol. 178(1), pages 173-200, July.
    11. Barbour, A. D. & Utev, Sergey, 2004. "Approximating the Reed-Frost epidemic process," Stochastic Processes and their Applications, Elsevier, vol. 113(2), pages 173-197, October.
    12. Sáenz-Royo, Carlos & Lozano-Rojo, Álvaro, 2023. "Authoritarianism versus participation in innovation decisions," Technovation, Elsevier, vol. 124(C).
    13. Vilches, T.N. & Esteva, L. & Ferreira, C.P., 2019. "Disease persistence and serotype coexistence: An expected feature of human mobility," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 161-172.
    14. Tomovski, Igor & Kocarev, Ljupčo, 2015. "Network topology inference from infection statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 272-285.
    15. Youzhong Wang & Daniel Zeng & Bin Zhu & Xiaolong Zheng & Feiyue Wang, 2014. "Patterns of news dissemination through online news media: A case study in China," Information Systems Frontiers, Springer, vol. 16(4), pages 557-570, September.
    16. Li, Xun & Cao, Lang, 2016. "Diffusion processes of fragmentary information on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 624-634.
    17. Hüseyin İkizler, 2019. "Contagion of network products in small-world networks," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(4), pages 789-809, December.
    18. Liu, Yun & Diao, Su-Meng & Zhu, Yi-Xiang & Liu, Qing, 2016. "SHIR competitive information diffusion model for online social media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 543-553.
    19. Guillaume, Jean-Loup & Latapy, Matthieu, 2006. "Bipartite graphs as models of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 795-813.
    20. Foti, Nicholas J. & Pauls, Scott & Rockmore, Daniel N., 2013. "Stability of the World Trade Web over time – An extinction analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 37(9), pages 1889-1910.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:107:y:2003:i:2:p:233-268. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.