28,024 research outputs found
Epidemic Spreading with External Agents
We study epidemic spreading processes in large networks, when the spread is
assisted by a small number of external agents: infection sources with bounded
spreading power, but whose movement is unrestricted vis-\`a-vis the underlying
network topology. For networks which are `spatially constrained', we show that
the spread of infection can be significantly speeded up even by a few such
external agents infecting randomly. Moreover, for general networks, we derive
upper-bounds on the order of the spreading time achieved by certain simple
(random/greedy) external-spreading policies. Conversely, for certain common
classes of networks such as line graphs, grids and random geometric graphs, we
also derive lower bounds on the order of the spreading time over all
(potentially network-state aware and adversarial) external-spreading policies;
these adversarial lower bounds match (up to logarithmic factors) the spreading
time achieved by an external agent with a random spreading policy. This
demonstrates that random, state-oblivious infection-spreading by an external
agent is in fact order-wise optimal for spreading in such spatially constrained
networks
Epidemic Thresholds with External Agents
We study the effect of external infection sources on phase transitions in
epidemic processes. In particular, we consider an epidemic spreading on a
network via the SIS/SIR dynamics, which in addition is aided by external agents
- sources unconstrained by the graph, but possessing a limited infection rate
or virulence. Such a model captures many existing models of externally aided
epidemics, and finds use in many settings - epidemiology, marketing and
advertising, network robustness, etc. We provide a detailed characterization of
the impact of external agents on epidemic thresholds. In particular, for the
SIS model, we show that any external infection strategy with constant virulence
either fails to significantly affect the lifetime of an epidemic, or at best,
sustains the epidemic for a lifetime which is polynomial in the number of
nodes. On the other hand, a random external-infection strategy, with rate
increasing linearly in the number of infected nodes, succeeds under some
conditions to sustain an exponential epidemic lifetime. We obtain similar sharp
thresholds for the SIR model, and discuss the relevance of our results in a
variety of settings.Comment: 12 pages, 2 figures (to appear in INFOCOM 2014
From Public Outrage to the Burst of Public Violence: An Epidemic-Like Model
This study extends classical models of spreading epidemics to describe the
phenomenon of contagious public outrage, which eventually leads to the spread
of violence following a disclosure of some unpopular political decisions and/or
activity. Accordingly, a mathematical model is proposed to simulate from the
start, the internal dynamics by which an external event is turned into internal
violence within a population. Five kinds of agents are considered: "Upset" (U),
"Violent" (V), "Sensitive" (S), "Immune" (I), and "Relaxed" (R), leading to a
set of ordinary differential equations, which in turn yield the dynamics of
spreading of each type of agents among the population. The process is stopped
with the deactivation of the associated issue. Conditions coinciding with a
twofold spreading of public violence are singled out. The results shed a new
light to understand terror activity and provides some hint on how to curb the
spreading of violence within population globally sensitive to specific world
issues. Recent world violent events are discussed.Comment: 22 pages, 9 figure
Effect of Coupling on the Epidemic Threshold in Interconnected Complex Networks: A Spectral Analysis
In epidemic modeling, the term infection strength indicates the ratio of
infection rate and cure rate. If the infection strength is higher than a
certain threshold -- which we define as the epidemic threshold - then the
epidemic spreads through the population and persists in the long run. For a
single generic graph representing the contact network of the population under
consideration, the epidemic threshold turns out to be equal to the inverse of
the spectral radius of the contact graph. However, in a real world scenario it
is not possible to isolate a population completely: there is always some
interconnection with another network, which partially overlaps with the contact
network. Results for epidemic threshold in interconnected networks are limited
to homogeneous mixing populations and degree distribution arguments. In this
paper, we adopt a spectral approach. We show how the epidemic threshold in a
given network changes as a result of being coupled with another network with
fixed infection strength. In our model, the contact network and the
interconnections are generic. Using bifurcation theory and algebraic graph
theory, we rigorously derive the epidemic threshold in interconnected networks.
These results have implications for the broad field of epidemic modeling and
control. Our analytical results are supported by numerical simulations.Comment: 7 page
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