210 research outputs found
Efficient Immunization Strategies for Computer Networks and Populations
We present an effective immunization strategy for computer networks and
populations with broad and, in particular, scale-free degree distributions. The
proposed strategy, acquaintance immunization, calls for the immunization of
random acquaintances of random nodes (individuals). The strategy requires no
knowledge of the node degrees or any other global knowledge, as do targeted
immunization strategies. We study analytically the critical threshold for
complete immunization. We also study the strategy with respect to the
susceptible-infected-removed epidemiological model. We show that the
immunization threshold is dramatically reduced with the suggested strategy, for
all studied cases.Comment: Revtex, 5 pages, 4 ps fig
Arrival Time Statistics in Global Disease Spread
Metapopulation models describing cities with different populations coupled by
the travel of individuals are of great importance in the understanding of
disease spread on a large scale. An important example is the Rvachev-Longini
model [{\it Math. Biosci.} {\bf 75}, 3-22 (1985)] which is widely used in
computational epidemiology. Few analytical results are however available and in
particular little is known about paths followed by epidemics and disease
arrival times. We study the arrival time of a disease in a city as a function
of the starting seed of the epidemics. We propose an analytical Ansatz, test it
in the case of a spreading on the world wide air transportation network, and
show that it predicts accurately the arrival order of a disease in world-wide
cities
Immunization of networks with community structure
In this study, an efficient method to immunize modular networks (i.e.,
networks with community structure) is proposed. The immunization of networks
aims at fragmenting networks into small parts with a small number of removed
nodes. Its applications include prevention of epidemic spreading, intentional
attacks on networks, and conservation of ecosystems. Although preferential
immunization of hubs is efficient, good immunization strategies for modular
networks have not been established. On the basis of an immunization strategy
based on the eigenvector centrality, we develop an analytical framework for
immunizing modular networks. To this end, we quantify the contribution of each
node to the connectivity in a coarse-grained network among modules. We verify
the effectiveness of the proposed method by applying it to model and real
networks with modular structure.Comment: 3 figures, 1 tabl
Velocity and hierarchical spread of epidemic outbreaks in scale-free networks
We study the effect of the connectivity pattern of complex networks on the
propagation dynamics of epidemics. The growth time scale of outbreaks is
inversely proportional to the network degree fluctuations, signaling that
epidemics spread almost instantaneously in networks with scale-free degree
distributions. This feature is associated with an epidemic propagation that
follows a precise hierarchical dynamics. Once the highly connected hubs are
reached, the infection pervades the network in a progressive cascade across
smaller degree classes. The present results are relevant for the development of
adaptive containment strategies.Comment: 4 pages, 4 figures, final versio
Epidemic variability in complex networks
We study numerically the variability of the outbreak of diseases on complex
networks. We use a SI model to simulate the disease spreading at short times,
in homogeneous and in scale-free networks. In both cases, we study the effect
of initial conditions on the epidemic's dynamics and its variability. The
results display a time regime during which the prevalence exhibits a large
sensitivity to noise. We also investigate the dependence of the infection time
on nodes' degree and distance to the seed. In particular, we show that the
infection time of hubs have large fluctuations which limit their reliability as
early-detection stations. Finally, we discuss the effect of the multiplicity of
shortest paths between two nodes on the infection time. Furthermore, we
demonstrate that the existence of even longer paths reduces the average
infection time. These different results could be of use for the design of
time-dependent containment strategies
Migration paths saturations in meta-epidemic systems
In this paper we consider a simple two-patch model in which a population
affected by a disease can freely move. We assume that the capacity of the
interconnected paths is limited, and thereby influencing the migration rates.
Possible habitat disruptions due to human activities or natural events are
accounted for. The demographic assumptions prevent the ecosystem to be wiped
out, and the disease remains endemic in both populated patches at a stable
equilibrium, but possibly also with an oscillatory behavior in the case of
unidirectional migrations. Interestingly, if infected cannot migrate, it is
possible that one patch becomes disease-free. This fact could be exploited to
keep disease-free at least part of the population
Heterogeneity in connectivity of habitat networks saves stable coexistence of competing species
Coexistence of individuals with different species or phenotypes is often
found in nature in spite of competition between them. Stable coexistence of
multiple types of individuals have implications for maintenance of ecological
biodiversity and emergence of altruism in society, to name a few. Various
mechanisms of coexistence including spatial structure of populations,
heterogeneous individuals, and heterogeneous environments, have been proposed.
In reality, individuals disperse and interact on complex networks. We examine
how heterogeneous degree distributions of networks influence coexistence,
focusing on models of cyclically competing species. We show analytically and
numerically that heterogeneity in degree distributions promotes stable
coexistence.Comment: 4 figure
Monte Carlo simulation of the transmission of measles: Beyond the mass action principle
We present a Monte Carlo simulation of the transmission of measles within a
population sample during its growing and equilibrium states by introducing two
different vaccination schedules of one and two doses. We study the effects of
the contact rate per unit time as well as the initial conditions on the
persistence of the disease. We found a weak effect of the initial conditions
while the disease persists when lies in the range 1/L-10/L ( being
the latent period). Further comparison with existing data, prediction of future
epidemics and other estimations of the vaccination efficiency are provided.
Finally, we compare our approach to the models using the mass action
principle in the first and another epidemic region and found the incidence
independent of the number of susceptibles after the epidemic peak while it
strongly fluctuates in its growing region. This method can be easily applied to
other human, animals and vegetable diseases and includes more complicated
parameters.Comment: 15 pages, 4 figures, 1 table, Submitted to Phys.Rev.
Size of Outbreaks Near the Epidemic Threshold
The spread of infectious diseases near the epidemic threshold is
investigated. Scaling laws for the size and the duration of outbreaks
originating from a single infected individual in a large susceptible population
are obtained. The maximal size of an outbreak n_* scales as N^{2/3} with N the
population size. This scaling law implies that the average outbreak size
scales as N^{1/3}. Moreover, the maximal and the average duration of an
outbreak grow as t_* ~ N^{1/3} and ~ ln N, respectively.Comment: 4 pages, 5 figure
Epidemic dynamics in finite size scale-free networks
Many real networks present a bounded scale-free behavior with a connectivity
cut-off due to physical constraints or a finite network size. We study epidemic
dynamics in bounded scale-free networks with soft and hard connectivity
cut-offs. The finite size effects introduced by the cut-off induce an epidemic
threshold that approaches zero at increasing sizes. The induced epidemic
threshold is very small even at a relatively small cut-off, showing that the
neglection of connectivity fluctuations in bounded scale-free networks leads to
a strong over-estimation of the epidemic threshold. We provide the expression
for the infection prevalence and discuss its finite size corrections. The
present work shows that the highly heterogeneous nature of scale-free networks
does not allow the use of homogeneous approximations even for systems of a
relatively small number of nodes.Comment: 4 pages, 2 eps figure
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