Giuseppe
Emeritus
[Source: Proceedings of the National Academy of Sciences of the United States of America, full page: (LINK). Abstract, edited.]
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Spatial extent of an outbreak in animal epidemics
Eric Dumonteil<SUP>a</SUP>, Satya N. Majumdar<SUP>b</SUP>, Alberto Rosso<SUP>b</SUP>,<SUP>1</SUP>, and Andrea Zoia<SUP>a</SUP>
<SUP></SUP>
Author Affiliations: <SUP>a</SUP>DEN/DM2S/SERMA/LTSD, Commissariat ? l?Energie Atomique/Saclay, 91191 Gif-sur-Yvette Cedex, France; and <SUP>b</SUP>Unit? Mixte de Recherche 8626, Centre National de la Recherche Scientifique?Universit? Paris-Sud, LPTMS, 91405 Orsay Cedex, France
Edited by Susan N. Coppersmith, University of Wisconsin, Madison, WI, and approved January 29, 2013 (received for review July 31, 2012)
Abstract
Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, and therefore, fluctuations around their average are important: then, it is commonly assumed that the susceptible?infected?recovered mechanism can be described by a stochastic birth?death process of Galton?Watson type. The displacements of the infected individuals can be modeled by resorting to Brownian motion, which is applicable when long-range movements and complex network interactions can be safely neglected, like in the case of animal epidemics. In this context, the spatial extent of an epidemic can be assessed by computing the convex hull enclosing the infected individuals at a given time. We derive the exact evolution equations for the mean perimeter and the mean area of the convex hull, and we compare them with Monte Carlo simulations.
branching Brownian motion - extreme value statistics
Footnotes
<SUP>1</SUP>To whom correspondence should be addressed. E-mail: alberto.rosso@u-psud.fr.
Author contributions: E.D., S.N.M., A.R., and A.Z. performed research and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1213237110/-/DCSupplemental.
-Eric Dumonteil<SUP>a</SUP>, Satya N. Majumdar<SUP>b</SUP>, Alberto Rosso<SUP>b</SUP>,<SUP>1</SUP>, and Andrea Zoia<SUP>a</SUP>
<SUP></SUP>
Author Affiliations: <SUP>a</SUP>DEN/DM2S/SERMA/LTSD, Commissariat ? l?Energie Atomique/Saclay, 91191 Gif-sur-Yvette Cedex, France; and <SUP>b</SUP>Unit? Mixte de Recherche 8626, Centre National de la Recherche Scientifique?Universit? Paris-Sud, LPTMS, 91405 Orsay Cedex, France
Edited by Susan N. Coppersmith, University of Wisconsin, Madison, WI, and approved January 29, 2013 (received for review July 31, 2012)
Abstract
Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, and therefore, fluctuations around their average are important: then, it is commonly assumed that the susceptible?infected?recovered mechanism can be described by a stochastic birth?death process of Galton?Watson type. The displacements of the infected individuals can be modeled by resorting to Brownian motion, which is applicable when long-range movements and complex network interactions can be safely neglected, like in the case of animal epidemics. In this context, the spatial extent of an epidemic can be assessed by computing the convex hull enclosing the infected individuals at a given time. We derive the exact evolution equations for the mean perimeter and the mean area of the convex hull, and we compare them with Monte Carlo simulations.
branching Brownian motion - extreme value statistics
Footnotes
<SUP>1</SUP>To whom correspondence should be addressed. E-mail: alberto.rosso@u-psud.fr.
Author contributions: E.D., S.N.M., A.R., and A.Z. performed research and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1213237110/-/DCSupplemental.
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