Document Detail

Cluster approximations for infection dynamics on random networks.
MedLine Citation:
PMID:  20365014     Owner:  NLM     Status:  MEDLINE    
In this paper, we consider a simple stochastic epidemic model on large regular random graphs and the stochastic process that corresponds to this dynamics in the standard pair approximation. Using the fact that the nodes of a pair are unlikely to share neighbors, we derive the master equation for this process and obtain from the system size expansion the power spectrum of the fluctuations in the quasistationary state. We show that whenever the pair approximation deterministic equations give an accurate description of the behavior of the system in the thermodynamic limit, the power spectrum of the fluctuations measured in long simulations is well approximated by the analytical power spectrum. If this assumption breaks down, then the cluster approximation must be carried out beyond the level of pairs. We construct an uncorrelated triplet approximation that captures the behavior of the system in a region of parameter space where the pair approximation fails to give a good quantitative or even qualitative agreement. For these parameter values, the power spectrum of the fluctuations in finite systems can be computed analytically from the master equation of the corresponding stochastic process.
G Rozhnova; A Nunes
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Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't     Date:  2009-11-20
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  80     ISSN:  1550-2376     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2009 Nov 
Date Detail:
Created Date:  2010-04-06     Completed Date:  2010-07-14     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  051915     Citation Subset:  IM    
Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências da Universidade de Lisboa, P-1649-003 Lisboa Codex, Portugal.
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MeSH Terms
Cluster Analysis
Communicable Diseases / epidemiology*,  physiopathology*
Computer Simulation
Disease Outbreaks / statistics & numerical data*
Models, Biological*
Proportional Hazards Models*
Risk Assessment / methods
Risk Factors
Stochastic Processes

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine

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