Stochastic oscillations of adaptive networks: application to epidemic modelling

Tim Rogers, William Clifford-Brown, Cat Mills, Tobias Galla

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can radically alter the systems behaviour. In this paper we develop a method to predict the effects of stochasticity in adaptive networks by making use of a pair-based proxy model. The technique is developed in the context of an epidemiological model of a disease spreading over an adaptive network of infectious contact. Our analysis reveals that in this model the structure of the network exhibits stochastic oscillations in response to fluctuations in the disease dynamic. 

Original languageEnglish
Article numberP08018
Number of pages15
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2012
Issue number8
DOIs
Publication statusPublished - Aug 2012
Externally publishedYes

Keywords

  • epidemic modelling
  • network dynamics
  • stochastic processes

Cite this

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Stochastic oscillations of adaptive networks : application to epidemic modelling. / Rogers, Tim; Clifford-Brown, William; Mills, Cat; Galla, Tobias.

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, No. 8, P08018, 08.2012.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Clifford-Brown, William

AU - Mills, Cat

AU - Galla, Tobias

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AB - Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can radically alter the systems behaviour. In this paper we develop a method to predict the effects of stochasticity in adaptive networks by making use of a pair-based proxy model. The technique is developed in the context of an epidemiological model of a disease spreading over an adaptive network of infectious contact. Our analysis reveals that in this model the structure of the network exhibits stochastic oscillations in response to fluctuations in the disease dynamic. 

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KW - network dynamics

KW - stochastic processes

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