9,005 research outputs found
Stochastic effects in a seasonally forced epidemic model
The interplay of seasonality, the system's nonlinearities and intrinsic
stochasticity is studied for a seasonally forced
susceptible-exposed-infective-recovered stochastic model. The model is explored
in the parameter region that corresponds to childhood infectious diseases such
as measles. The power spectrum of the stochastic fluctuations around the
attractors of the deterministic system that describes the model in the
thermodynamic limit is computed analytically and validated by stochastic
simulations for large system sizes. Size effects are studied through additional
simulations. Other effects such as switching between coexisting attractors
induced by stochasticity often mentioned in the literature as playing an
important role in the dynamics of childhood infectious diseases are also
investigated. The main conclusion is that stochastic amplification, rather than
these effects, is the key ingredient to understand the observed incidence
patterns.Comment: 13 pages, 9 figures, 3 table
Population dynamics on random networks: simulations and analytical models
We study the phase diagram of the standard pair approximation equations for
two different models in population dynamics, the
susceptible-infective-recovered-susceptible model of infection spread and a
predator-prey interaction model, on a network of homogeneous degree . These
models have similar phase diagrams and represent two classes of systems for
which noisy oscillations, still largely unexplained, are observed in nature. We
show that for a certain range of the parameter both models exhibit an
oscillatory phase in a region of parameter space that corresponds to weak
driving. This oscillatory phase, however, disappears when is large. For
, we compare the phase diagram of the standard pair approximation
equations of both models with the results of simulations on regular random
graphs of the same degree. We show that for parameter values in the oscillatory
phase, and even for large system sizes, the simulations either die out or
exhibit damped oscillations, depending on the initial conditions. We discuss
this failure of the standard pair approximation model to capture even the
qualitative behavior of the simulations on large regular random graphs and the
relevance of the oscillatory phase in the pair approximation diagrams to
explain the cycling behavior found in real populations.Comment: 8 pages, 5 figures; we have expanded and rewritten the introduction,
slightly modified the abstract and the text in other sections; also, several
new references have been added in the revised manuscript (Refs.
[17-25,30,35])
Detecting and Describing Dynamic Equilibria in Adaptive Networks
We review modeling attempts for the paradigmatic contact process (or SIS
model) on adaptive networks. Elaborating on one particular proposed mechanism
of topology change (rewiring) and its mean field analysis, we obtain a
coarse-grained view of coevolving network topology in the stationary active
phase of the system. Introducing an alternative framework applicable to a wide
class of adaptive networks, active stationary states are detected, and an
extended description of the resulting steady-state statistics is given for
three different rewiring schemes. We find that slight modifications of the
standard rewiring rule can result in either minuscule or drastic change of
steady-state network topologies.Comment: 14 pages, 10 figures; typo in the third of Eqs. (1) correcte
Pair Approximation Models for Disease Spread
We consider a Susceptible-Infective-Recovered (SIR) model, where the
mechanism for the renewal of susceptibles is demographic, on a ring with next
nearest neighbour interactions, and a family of correlated pair approximations
(CPA), parametrized by a measure of the relative contributions of loops and
open triplets of the sites involved in the infection process. We have found
that the phase diagram of the CPA, at fixed coordination number, changes
qualitatively as the relative weight of the loops increases, from the phase
diagram of the uncorrelated pair approximation to phase diagrams typical of
one-dimensional systems. In addition, we have performed computer simulations of
the same model and shown that while the CPA with a constant correlation
parameter cannot describe the global behaviour of the model, a reasonable
description of the endemic equilibria as well as of the phase diagram may be
obtained by allowing the parameter to depend on the demographic rate.Comment: 6 pages, 3 figures, LaTeX2e+SVJour+AmSLaTeX, NEXTSigmaPhi 2005;
metadata title corrected wrt paper titl
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