5,754 research outputs found
Quarantine generated phase transition in epidemic spreading
We study the critical effect of quarantine on the propagation of epidemics on
an adaptive network of social contacts. For this purpose, we analyze the
susceptible-infected-recovered (SIR) model in the presence of quarantine, where
susceptible individuals protect themselves by disconnecting their links to
infected neighbors with probability w, and reconnecting them to other
susceptible individuals chosen at random. Starting from a single infected
individual, we show by an analytical approach and simulations that there is a
phase transition at a critical rewiring (quarantine) threshold w_c separating a
phase (w<w_c) where the disease reaches a large fraction of the population,
from a phase (w >= w_c) where the disease does not spread out. We find that in
our model the topology of the network strongly affects the size of the
propagation, and that w_c increases with the mean degree and heterogeneity of
the network. We also find that w_c is reduced if we perform a preferential
rewiring, in which the rewiring probability is proportional to the degree of
infected nodes.Comment: 13 pages, 6 figure
Invited review: Epidemics on social networks
Since its first formulations almost a century ago, mathematical models for
disease spreading contributed to understand, evaluate and control the epidemic
processes.They promoted a dramatic change in how epidemiologists thought of the
propagation of infectious diseases.In the last decade, when the traditional
epidemiological models seemed to be exhausted, new types of models were
developed.These new models incorporated concepts from graph theory to describe
and model the underlying social structure.Many of these works merely produced a
more detailed extension of the previous results, but some others triggered a
completely new paradigm in the mathematical study of epidemic processes. In
this review, we will introduce the basic concepts of epidemiology, epidemic
modeling and networks, to finally provide a brief description of the most
relevant results in the field.Comment: 17 pages, 13 figure
Economic and social factors in designing disease control strategies for epidemics on networks
Models for control of epidemics on local, global and small-world networks are
considered, with only partial information accessible about the status of
individuals and their connections. The main goal of an effective control
measure is to stop the epidemic at a lowest possible cost, including treatment
and cost necessary to track the disease spread. We show that delay in detection
of infectious individuals and presence of long-range links are the most
important factors determining the cost. However, the details of long-range
links are usually the least-known element of the social interactions due to
their occasional character and potentially short life-span. We show that under
some conditions on the probability of disease spread, it is advisable to
attempt to track those links. Thus, collecting some additional knowledge about
the network structure might be beneficial to ensure a successful and
cost-effective control.Comment: To be published in Acta Phys. Pol.
A class of pairwise models for epidemic dynamics on weighted networks
In this paper, we study the (susceptible-infected-susceptible) and
(susceptible-infected-removed) epidemic models on undirected, weighted
networks by deriving pairwise-type approximate models coupled with
individual-based network simulation. Two different types of
theoretical/synthetic weighted network models are considered. Both models start
from non-weighted networks with fixed topology followed by the allocation of
link weights in either (i) random or (ii) fixed/deterministic way. The pairwise
models are formulated for a general discrete distribution of weights, and these
models are then used in conjunction with network simulation to evaluate the
impact of different weight distributions on epidemic threshold and dynamics in
general. For the dynamics, the basic reproductive ratio is
computed, and we show that (i) for both network models is maximised if
all weights are equal, and (ii) when the two models are equally matched, the
networks with a random weight distribution give rise to a higher value.
The models are also used to explore the agreement between the pairwise and
simulation models for different parameter combinations
Worm Epidemics in Wireless Adhoc Networks
A dramatic increase in the number of computing devices with wireless
communication capability has resulted in the emergence of a new class of
computer worms which specifically target such devices. The most striking
feature of these worms is that they do not require Internet connectivity for
their propagation but can spread directly from device to device using a
short-range radio communication technology, such as WiFi or Bluetooth. In this
paper, we develop a new model for epidemic spreading of these worms and
investigate their spreading in wireless ad hoc networks via extensive Monte
Carlo simulations. Our studies show that the threshold behaviour and dynamics
of worm epidemics in these networks are greatly affected by a combination of
spatial and temporal correlations which characterize these networks, and are
significantly different from the previously studied epidemics in the Internet
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