Stochastic oscillations of adaptive networks: application to epidemic modelling

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 system's behaviour. In this article 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.

11 pages, 4 figures

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• Rare Event Extinction on Stochastic Networks
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• Macroscopic approximation methods for the analysis of adaptive networked agent-based models: The example of a two-sector investment model