Estimation of the infection parameter in the different phases of an epidemic modeled by a branching process

  • The aim of this paper is to build and compare estimators of the infection parameter in the different phases of an epidemic (growth and extinction phases). The epidemic is modeled by a Markovian process of order d > 1 (allowing non-Markovian life spans), and can be written as a multitype branching process. We propose three estimators suitable for the different classes of criticality of the process, in particular for the subcritical case corresponding to the extinction phase. We prove their consistency and asymptotic normality for two asymptotics, when the number of ancestors (resp. number of generations) tends to infinity. We illustrate the asymptotic properties with simulated examples, and finally use our estimators to study the infection intensity in the extinction phase of the BSE epidemic in Great-Britain.

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Metadaten
Author:Sophie Pénisson
URN:urn:nbn:de:kobv:517-opus-49607
Series (Serial Number):Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint (2010, 04)
Document Type:Preprint
Language:English
Date of Publication (online):2011/03/31
Year of Completion:2010
Publishing Institution:Universität Potsdam
Release Date:2011/03/31
RVK - Regensburg Classification:SI 990
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Collections:Universität Potsdam / Aufsätze (Pre- und Postprints) / Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik / Wahrscheinlichkeitstheorie
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht