Stochastic oscillations of adaptive networks: application to epidemic modelling

TL;DR

This paper introduces a pair-based proxy model to predict stochastic effects in adaptive networks, revealing that intrinsic noise can induce oscillations in network structure during disease spread.

Contribution

The study develops a novel method to analyze stochasticity in adaptive networks, specifically applied to epidemiological models, highlighting the impact of intrinsic noise on network dynamics.

Findings

Network structure exhibits stochastic oscillations due to disease fluctuations.

Intrinsic noise significantly alters the behavior predicted by deterministic models.

The pair-based proxy effectively predicts stochastic effects in adaptive networks.

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.