1,180 research outputs found
Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation
We investigate saturation effects in susceptible-infected-susceptible (SIS)
models of the spread of epidemics in heterogeneous populations. The structure
of interactions in the population is represented by networks with connectivity
distribution ,including scale-free(SF) networks with power law
distributions . Considering cases where the transmission
of infection between nodes depends on their connectivity, we introduce a
saturation function which reduces the infection transmission rate
across an edge going from a node with high connectivity . A mean
field approximation with the neglect of degree-degree correlation then leads to
a finite threshold for SF networks with . We
also find, in this approximation, the fraction of infected individuals among
those with degree for close to . We investigate via
computer simulation the contact process on a heterogeneous regular lattice and
compare the results with those obtained from mean field theory with and without
neglect of degree-degree correlations.Comment: 6 figure
Effects of aging and links removal on epidemic dynamics in scale-free networks
We study the combined effects of aging and links removal on epidemic dynamics
in the Barab\'{a}si-Albert scale-free networks. The epidemic is described by a
susceptible-infected-refractory (SIR) model. The aging effect of a node
introduced at time is described by an aging factor of the form
in the probability of being connected to newly added nodes
in a growing network under the preferential attachment scheme based on
popularity of the existing nodes. SIR dynamics is studied in networks with a
fraction of the links removed. Extensive numerical simulations reveal
that there exists a threshold such that for , epidemic
breaks out in the network. For , only a local spread results. The
dependence of on is studied in detail. The function
separates the space formed by and into regions
corresponding to local and global spreads, respectively.Comment: 8 pages, 3 figures, revtex, corrected Ref.[11
Immunization for complex network based on the effective degree of vertex
The basic idea of many effective immunization strategies is first to rank the
importance of vertices according to the degrees of vertices and then remove the
vertices from highest importance to lowest until the network becomes
disconnected. Here we define the effective degrees of vertex, i.e., the number
of its connections linking to un-immunized nodes in current network during the
immunization procedure, to rank the importance of vertex, and modify these
strategies by using the effective degrees of vertices. Simulations on both the
scale-free network models with various degree correlations and two real
networks have revealed that the immunization strategies based on the effective
degrees are often more effective than those based on the degrees in the initial
network.Comment: 16 pages, 5 figure
Population Dynamics in Spatially Heterogeneous Systems with Drift: the generalized contact process
We investigate the time evolution and stationary states of a stochastic,
spatially discrete, population model (contact process) with spatial
heterogeneity and imposed drift (wind) in one- and two-dimensions. We consider
in particular a situation in which space is divided into two regions: an oasis
and a desert (low and high death rates). Carrying out computer simulations we
find that the population in the (quasi) stationary state will be zero,
localized, or delocalized, depending on the values of the drift and other
parameters. The phase diagram is similar to that obtained by Nelson and
coworkers from a deterministic, spatially continuous model of a bacterial
population undergoing convection in a heterogeneous medium.Comment: 8 papes, 12 figure
Epidemic threshold in structured scale-free networks
We analyze the spreading of viruses in scale-free networks with high
clustering and degree correlations, as found in the Internet graph. For the
Suscetible-Infected-Susceptible model of epidemics the prevalence undergoes a
phase transition at a finite threshold of the transmission probability.
Comparing with the absence of a finite threshold in networks with purely random
wiring, our result suggests that high clustering and degree correlations
protect scale-free networks against the spreading of viruses. We introduce and
verify a quantitative description of the epidemic threshold based on the
connectivity of the neighborhoods of the hubs.Comment: 4 pages, 4 figure
A generic map has no absolutely continuous invariant probability measure
Let be a smooth compact manifold (maybe with boundary, maybe
disconnected) of any dimension . We consider the set of maps
which have no absolutely continuous (with respect to Lebesgue)
invariant probability measure. We show that this is a residual (dense
C^1$ topology.
In the course of the proof, we need a generalization of the usual Rokhlin
tower lemma to non-invariant measures. That result may be of independent
interest.Comment: 12 page
Epidemics in Networks of Spatially Correlated Three-dimensional Root Branching Structures
Using digitized images of the three-dimensional, branching structures for
root systems of bean seedlings, together with analytical and numerical methods
that map a common 'SIR' epidemiological model onto the bond percolation
problem, we show how the spatially-correlated branching structures of plant
roots affect transmission efficiencies, and hence the invasion criterion, for a
soil-borne pathogen as it spreads through ensembles of morphologically complex
hosts. We conclude that the inherent heterogeneities in transmissibilities
arising from correlations in the degrees of overlap between neighbouring
plants, render a population of root systems less susceptible to epidemic
invasion than a corresponding homogeneous system. Several components of
morphological complexity are analysed that contribute to disorder and
heterogeneities in transmissibility of infection. Anisotropy in root shape is
shown to increase resilience to epidemic invasion, while increasing the degree
of branching enhances the spread of epidemics in the population of roots. Some
extension of the methods for other epidemiological systems are discussed.Comment: 21 pages, 8 figure
Complex population dynamics as a competition between multiple time-scale phenomena
The role of the selection pressure and mutation amplitude on the behavior of
a single-species population evolving on a two-dimensional lattice, in a
periodically changing environment, is studied both analytically and
numerically. The mean-field level of description allows to highlight the
delicate interplay between the different time-scale processes in the resulting
complex dynamics of the system. We clarify the influence of the amplitude and
period of the environmental changes on the critical value of the selection
pressure corresponding to a phase-transition "extinct-alive" of the population.
However, the intrinsic stochasticity and the dynamically-built in correlations
among the individuals, as well as the role of the mutation-induced variety in
population's evolution are not appropriately accounted for. A more refined
level of description, which is an individual-based one, has to be considered.
The inherent fluctuations do not destroy the phase transition "extinct-alive",
and the mutation amplitude is strongly influencing the value of the critical
selection pressure. The phase diagram in the plane of the population's
parameters -- selection and mutation is discussed as a function of the
environmental variation characteristics. The differences between a smooth
variation of the environment and an abrupt, catastrophic change are also
addressesd.Comment: 15 pages, 12 figures. Accepted for publication in Phys. Rev.
Oscillations in low-dimensional cyclic differential delay systems
Nonlinear autonomous N-dimensional systems of cyclic differential equations with delays and overall negative feedback are considered. Such systems serve as mathematical models of numerous real world phenomena in physics and laser optics, physiology and mathematical biology, economics and life sciences among others. In the case of lower dimensions and sufficient conditions are derived for the oscillation of all solutions about the unique equilibrium. Open problems and conjectures are discussed for the higher dimensional case and for more convoluted sign feedbacks. © 2018, Springer Nature Switzerland AG
Polymorphic evolution sequence and evolutionary branching
We are interested in the study of models describing the evolution of a
polymorphic population with mutation and selection in the specific scales of
the biological framework of adaptive dynamics. The population size is assumed
to be large and the mutation rate small. We prove that under a good combination
of these two scales, the population process is approximated in the long time
scale of mutations by a Markov pure jump process describing the successive
trait equilibria of the population. This process, which generalizes the
so-called trait substitution sequence, is called polymorphic evolution
sequence. Then we introduce a scaling of the size of mutations and we study the
polymorphic evolution sequence in the limit of small mutations. From this study
in the neighborhood of evolutionary singularities, we obtain a full
mathematical justification of a heuristic criterion for the phenomenon of
evolutionary branching. To this end we finely analyze the asymptotic behavior
of 3-dimensional competitive Lotka-Volterra systems
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