Stochastic oscillations of adaptive networks: application to epidemic modelling

@article{Rogers2012StochasticOO,
  title={Stochastic oscillations of adaptive networks: application to epidemic modelling},
  author={Tim Rogers and William Clifford-Brown and Catherine G. Mills and Tobias Galla},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2012},
  volume={2012},
  pages={08018}
}
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 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… Expand
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References

SHOWING 1-10 OF 41 REFERENCES
Epidemic dynamics on an adaptive network.
TLDR
This work proposes a low-dimensional model to describe the epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by rewiring their network connections, and presents a full local bifurcation analysis. Expand
Stochastic amplification in epidemics
TLDR
A stochastic theory for the major dynamical transitions in epidemics from regular to irregular cycles is presented, which relies on the discrete nature of disease transmission and low spatial coupling to show how the amplification of noise varies across these transitions. Expand
Fluctuating epidemics on adaptive networks.
  • L. Shaw, I. Schwartz
  • Computer Science, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
TLDR
The introduction of rewiring affects both the network structure and the epidemic dynamics, and the average distance from a node to the nearest infective increases, which leads to regions of bistability where either an endemic or a disease-free steady state can exist. Expand
Stochastic oscillations in models of epidemics on a network of cities.
TLDR
The stochastic fluctuations in a susceptible-infected-recovered model of disease spread on a network of n cities are found to have an analogously simple dynamics: All oscillations have a single frequency, equal to that found in the one-city case. Expand
Correlation models for childhood epidemics
TLDR
Three pair models are introduced which attempt to capture the underlying heterogeneous structure of communicable disease by studying the connections and correlations between individuals, focusing on measles. Expand
Cluster approximations for infection dynamics on random networks.
  • G. Rozhnova, A. Nunes
  • Mathematics, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
TLDR
This paper constructs 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. Expand
Phase lag in epidemics on a network of cities.
TLDR
If the infection rate differs from city to city and the coupling between them is not too strong, these oscillations are synchronized with a well-defined phase lag between cities, and the analytic description of the effect is shown to be in good agreement with the results of stochastic simulations for realistic population sizes. Expand
Adaptive Networks: Theory, Models and Applications
With adaptive, complex networks, the evolution of the network topology and the dynamical processes on the network are equally important and often fundamentally entangled. Recent research has shownExpand
Sustained oscillations via coherence resonance in SIR.
TLDR
The nearly regular fluctuations in the infected and susceptible populations are described via an explicit construction of a stochastic amplitude equation and the agreement between the power spectral densities of the full model and the approximation verifies that coherence resonance is driving the behavior. Expand
Predator-prey cycles from resonant amplification of demographic stochasticity.
TLDR
This work presents the simplest individual level model of predator-prey dynamics and shows, via direct calculation, that it exhibits cycling behavior, indicating that additional biological mechanisms may not be necessary to explain observed predator- prey cycles in real (finite) populations. Expand
...
1
2
3
4
5
...