IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v55y1995i1p1-21.html
   My bibliography  Save this article

Strong approximations for epidemic models

Author

Listed:
  • Ball, Frank
  • Donnelly, Peter

Abstract

This paper is concerned with the approximation of early stages of epidemic processes by branching processes. A general model for an epidemic in a closed, homogeneously mixing population is presented. A construction of a sequence of such epidemics, indexed by the initial number of susceptibles N, from the limiting branching process is described. Strong convergence of the epidemic processes to the branching process is shown when the latter goes extinct. When the branching process does not go extinct, necessary and sufficient conditions on the sequence (tN) for strong convergence over the time interval [0, tN] are provided. Convergence of a wide variety of functionals of the epidemic process to corresponding functionals of the branching process is shown, and bounds are provided on the total variation distance for given N. The theory is illustrated by reference to the general stochastic epidemic. Generalisations to, for example, multipopulation epidemics are described briefly.

Suggested Citation

  • Ball, Frank & Donnelly, Peter, 1995. "Strong approximations for epidemic models," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 1-21, January.
    • Handle: RePEc:eee:spapps:v:55:y:1995:i:1:p:1-21
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(94)00034-Q
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Clancy, Damian & O'Neill, Philip, 1998. "Approximation of epidemics by inhomogeneous birth-and-death processes," Stochastic Processes and their Applications, Elsevier, vol. 73(2), pages 233-245, March.
    2. Demiris, Nikolaos & Kypraios, Theodore & Smith, L. Vanessa, 2012. "On the epidemic of financial crises," MPRA Paper 46693, University Library of Munich, Germany.
    3. Wierman, John C. & Marchette, David J., 2004. "Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction," Computational Statistics & Data Analysis, Elsevier, vol. 45(1), pages 3-23, February.
    4. 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.
    5. Chen, Zezhun & Dassios, Angelos & Kuan, Valerie & Lim, Jia Wei & Qu, Yan & Surya, Budhi & Zhao, Hongbiao, 2021. "A two-phase dynamic contagion model for COVID-19," LSE Research Online Documents on Economics 105064, London School of Economics and Political Science, LSE Library.
    6. Villela, Daniel A.M., 2016. "Analysis of the vectorial capacity of vector-borne diseases using moment-generating functions," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 1-8.
    7. Ball, Frank & Neal, Peter, 2003. "The great circle epidemic model," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 233-268, October.
    8. Johannes Müler & Volker Hösel, 2007. "Estimating the Tracing Probability from Contact History at the Onset of an Epidemic," Mathematical Population Studies, Taylor & Francis Journals, vol. 14(4), pages 211-236, November.
    9. Terrazas-Santamaria Diana & Mendoza-Palacios Saul & Berasaluce-Iza Julen, 2023. "An Alternative Approach to Frequency of Patent Technology Codes: The Case of Renewable Energy Generation," Economics - The Open-Access, Open-Assessment Journal, De Gruyter, vol. 17(1), pages 1-14, January.
    10. Simon, Matthieu, 2020. "SIR epidemics with stochastic infectious periods," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4252-4274.
    11. Claude Lefe`vre & Sergey Utev, 1999. "Branching Approximation for the Collective Epidemic Model," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 211-228, September.

    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:55:y:1995:i:1:p:1-21. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.