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Branching Approximation for the Collective Epidemic Model

Author

Listed:
  • Claude Lefe`vre

    (Universite´ Libre de Bruxelles)

  • Sergey Utev

    (La Trobe University)

Abstract

A new approach is developed that allows us to establish and analyze a branching-type approximation for the collective epidemic model. Firstly, a necessary and sufficient condition is obtained for the vague convergence of the final size of the epidemic to the total progeny in an appropriate branching model, as the initial number of susceptibles tends to infinity. Then, an upper bound for the L 1 distance between the statistics under study is derived, showing inter alia that the approximation may hold even when the initial number of infectives is arbitrarily large. The results are illustrated with several particular models of special interest.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:1:y:1999:i:2:d:10.1023_a:1010061321051
    DOI: 10.1023/A:1010061321051
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    References listed on IDEAS

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    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. Lefèvre, Claude & Utev, Sergei, 1997. "Mixed Poisson approximation in the collective epidemic model," Stochastic Processes and their Applications, Elsevier, vol. 69(2), pages 217-246, September.
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    Cited by:

    1. Donatien Hainaut, 2020. "An Actuarial Approach for Modeling Pandemic Risk," Risks, MDPI, vol. 9(1), pages 1-28, December.
    2. Hainaut, Donatien, 2020. "An actuarial approach for modeling pandemic risk," LIDAM Discussion Papers ISBA 2020025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. 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.

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