Document Detail


The abundance threshold for plague as a critical percolation phenomenon.
MedLine Citation:
PMID:  18668107     Owner:  NLM     Status:  MEDLINE    
Abstract/OtherAbstract:
Percolation theory is most commonly associated with the slow flow of liquid through a porous medium, with applications to the physical sciences. Epidemiological applications have been anticipated for disease systems where the host is a plant or volume of soil, and hence is fixed in space. However, no natural examples have been reported. The central question of interest in percolation theory, the possibility of an infinite connected cluster, corresponds in infectious disease to a positive probability of an epidemic. Archived records of plague (infection with Yersinia pestis) in populations of great gerbils (Rhombomys opimus) in Kazakhstan have been used to show that epizootics only occur when more than about 0.33 of the burrow systems built by the host are occupied by family groups. The underlying mechanism for this abundance threshold is unknown. Here we present evidence that it is a percolation threshold, which arises from the difference in scale between the movements that transport infectious fleas between family groups and the vast size of contiguous landscapes colonized by gerbils. Conventional theory predicts that abundance thresholds for the spread of infectious disease arise when transmission between hosts is density dependent such that the basic reproduction number (R(0)) increases with abundance, attaining 1 at the threshold. Percolation thresholds, however, are separate, spatially explicit thresholds that indicate long-range connectivity in a system and do not coincide with R(0) = 1. Abundance thresholds are the theoretical basis for attempts to manage infectious disease by reducing the abundance of susceptibles, including vaccination and the culling of wildlife. This first natural example of a percolation threshold in a disease system invites a re-appraisal of other invasion thresholds, such as those for epidemic viral infections in African lions (Panthera leo), and of other disease systems such as bovine tuberculosis (caused by Mycobacterium bovis) in badgers (Meles meles).
Authors:
S Davis; P Trapman; H Leirs; M Begon; J A P Heesterbeek
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Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't    
Journal Detail:
Title:  Nature     Volume:  454     ISSN:  1476-4687     ISO Abbreviation:  Nature     Publication Date:  2008 Jul 
Date Detail:
Created Date:  2008-07-31     Completed Date:  2008-08-11     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  0410462     Medline TA:  Nature     Country:  England    
Other Details:
Languages:  eng     Pagination:  634-7     Citation Subset:  IM    
Affiliation:
Theoretical Epidemiology, Faculty of Veterinary Medicine, University of Utrecht, Yalelaan 7, 3584 CL Utrecht, The Netherlands. S.A.Davis@uu.nl
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MeSH Terms
Descriptor/Qualifier:
Animals
Disease Outbreaks*
Fleas / microbiology,  physiology
Gerbillinae / microbiology,  parasitology
Kazakhstan / epidemiology
Models, Biological*
Plague / epidemiology,  parasitology,  transmission*,  veterinary
Population Density
Population Dynamics
Rodent Diseases / epidemiology,  parasitology,  transmission
Yersinia pestis / physiology*

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