Branching Approximation for the Collective Epidemic Model

Claude Lefe`vre and Sergey Utev
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Claude Lefe`vre: Universite´ Libre de Bruxelles
Sergey Utev: La Trobe University

Methodology and Computing in Applied Probability, 1999, vol. 1, issue 2, 211-228

Abstract: 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.

Keywords: Epidemic process; final size; branching process; total progeny; vague convergence; coupling; L 1 distance; total variation distance (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/A:1010061321051

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